Merge remote-tracking branch 'upstream-public/pr/1060' into development

ChangeLog

@@ -38,6 +38,19 @@ Features
 New deprecations
    * Deprecate usage of RSA primitives with non-matching key-type
      (e.g., signing with a public key).
+   * Direct manipulation of structure fields of RSA contexts is deprecated.
+     Users are advised to use the extended RSA API instead.
+
+API Changes
+   * Extend RSA interface by multiple functions allowing structure-
+     independent setup and export of RSA contexts. Most notably,
+     mbedtls_rsa_import and mbedtls_rsa_complete are introduced for setting
+     up RSA contexts from partial key material and having them completed to the
+     needs of the implementation automatically. This allows to setup private RSA
+     contexts from keys consisting of N,D,E only, even if P,Q are needed for the
+     purpose or CRT and/or blinding.
+   * The configuration option MBEDTLS_RSA_ALT can be used to define alternative
+     implementations of the RSA interface declared in rsa.h.
 
 Bugfix
    * Fix ssl_parse_record_header() to silently discard invalid DTLS records
@@ -89,6 +102,10 @@ Changes
    * Extend cert_write example program by options to set the CRT version
      and the message digest. Further, allow enabling/disabling of authority
      identifier, subject identifier and basic constraints extensions.
+   * Only check for necessary RSA structure fields in `mbedtls_rsa_private`. In
+     particular, don't require P,Q if neither CRT nor blinding are
+     used. Reported and fix proposed independently by satur9nine and sliai
+     on GitHub.
    * Only run AES-192 self-test if AES-192 is available. Fixes #963.
 
 = mbed TLS 2.6.0 branch released 2017-08-10

include/mbedtls/bignum.h

@@ -70,7 +70,7 @@
  * Maximum size of MPIs allowed in bits and bytes for user-MPIs.
  * ( Default: 512 bytes => 4096 bits, Maximum tested: 2048 bytes => 16384 bits )
  *
- * Note: Calculations can results temporarily in larger MPIs. So the number
+ * Note: Calculations can temporarily result in larger MPIs. So the number
  * of limbs required (MBEDTLS_MPI_MAX_LIMBS) is higher.
  */
 #define MBEDTLS_MPI_MAX_SIZE                              1024     /**< Maximum number of bytes for usable MPIs. */

include/mbedtls/config.h

@@ -270,14 +270,15 @@
 //#define MBEDTLS_CMAC_ALT
 //#define MBEDTLS_DES_ALT
 //#define MBEDTLS_GCM_ALT
-//#define MBEDTLS_XTEA_ALT
 //#define MBEDTLS_MD2_ALT
 //#define MBEDTLS_MD4_ALT
 //#define MBEDTLS_MD5_ALT
 //#define MBEDTLS_RIPEMD160_ALT
+//#define MBEDTLS_RSA_ALT
 //#define MBEDTLS_SHA1_ALT
 //#define MBEDTLS_SHA256_ALT
 //#define MBEDTLS_SHA512_ALT
+//#define MBEDTLS_XTEA_ALT
 /*
  * When replacing the elliptic curve module, pleace consider, that it is
  * implemented with two .c files:
@@ -1664,6 +1665,7 @@
  *          library/ecp.c
  *          library/ecdsa.c
  *          library/rsa.c
+ *          library/rsa_internal.c
  *          library/ssl_tls.c
  *
  * This module is required for RSA, DHM and ECC (ECDH, ECDSA) support.
@@ -2277,6 +2279,7 @@
  * Enable the RSA public-key cryptosystem.
  *
  * Module:  library/rsa.c
+ *          library/rsa_internal.c
  * Caller:  library/ssl_cli.c
  *          library/ssl_srv.c
  *          library/ssl_tls.c

include/mbedtls/rsa.h

@@ -68,14 +68,23 @@
  * The above constants may be used even if the RSA module is compile out,
  * eg for alternative (PKCS#11) RSA implemenations in the PK layers.
  */
-#if defined(MBEDTLS_RSA_C)
+
+#if !defined(MBEDTLS_RSA_ALT)
+// Regular implementation
+//
 
 #ifdef __cplusplus
 extern "C" {
 #endif
 
 /**
- * \brief          RSA context structure
+ * \brief   RSA context structure
+ *
+ * \note    Direct manipulation of the members of this structure
+ *          is deprecated and will no longer be supported starting
+ *          from the next major release. All manipulation should instead
+ *          be done through the public interface functions.
+ *
  */
 typedef struct
 {
@@ -88,19 +97,21 @@ typedef struct
     mbedtls_mpi D;                      /*!<  private exponent  */
     mbedtls_mpi P;                      /*!<  1st prime factor  */
     mbedtls_mpi Q;                      /*!<  2nd prime factor  */
+
     mbedtls_mpi DP;                     /*!<  D % (P - 1)       */
     mbedtls_mpi DQ;                     /*!<  D % (Q - 1)       */
     mbedtls_mpi QP;                     /*!<  1 / (Q % P)       */
 
     mbedtls_mpi RN;                     /*!<  cached R^2 mod N  */
+
     mbedtls_mpi RP;                     /*!<  cached R^2 mod P  */
     mbedtls_mpi RQ;                     /*!<  cached R^2 mod Q  */
 
     mbedtls_mpi Vi;                     /*!<  cached blinding value     */
     mbedtls_mpi Vf;                     /*!<  cached un-blinding value  */
 
-    int padding;                /*!<  MBEDTLS_RSA_PKCS_V15 for 1.5 padding and
+    int padding;                /*!<  \c MBEDTLS_RSA_PKCS_V15 for 1.5 padding and
-                                      MBEDTLS_RSA_PKCS_v21 for OAEP/PSS         */
+                                      \c MBEDTLS_RSA_PKCS_v21 for OAEP/PSS */
     int hash_id;                /*!<  Hash identifier of mbedtls_md_type_t as
                                       specified in the mbedtls_md.h header file
                                       for the EME-OAEP and EMSA-PSS
@@ -114,15 +125,15 @@ mbedtls_rsa_context;
 /**
  * \brief          Initialize an RSA context
  *
- *                 Note: Set padding to MBEDTLS_RSA_PKCS_V21 for the RSAES-OAEP
+ *                 Note: Set padding to \c MBEDTLS_RSA_PKCS_V21 for the RSAES-OAEP
  *                 encryption scheme and the RSASSA-PSS signature scheme.
  *
  * \param ctx      RSA context to be initialized
- * \param padding  MBEDTLS_RSA_PKCS_V15 or MBEDTLS_RSA_PKCS_V21
+ * \param padding  \c MBEDTLS_RSA_PKCS_V15 or \c MBEDTLS_RSA_PKCS_V21
- * \param hash_id  MBEDTLS_RSA_PKCS_V21 hash identifier
+ * \param hash_id  \c MBEDTLS_RSA_PKCS_V21 hash identifier
  *
  * \note           The hash_id parameter is actually ignored
- *                 when using MBEDTLS_RSA_PKCS_V15 padding.
+ *                 when using \c MBEDTLS_RSA_PKCS_V15 padding.
  *
  * \note           Choice of padding mode is strictly enforced for private key
  *                 operations, since there might be security concerns in
@@ -133,21 +144,241 @@ mbedtls_rsa_context;
  * \note           The chosen hash is always used for OEAP encryption.
  *                 For PSS signatures, it's always used for making signatures,
  *                 but can be overriden (and always is, if set to
- *                 MBEDTLS_MD_NONE) for verifying them.
+ *                 \c MBEDTLS_MD_NONE) for verifying them.
  */
 void mbedtls_rsa_init( mbedtls_rsa_context *ctx,
-               int padding,
+                       int padding,
-               int hash_id);
+                       int hash_id);
+
+/**
+ * \brief          Import a set of core parameters into an RSA context
+ *
+ * \param ctx      Initialized RSA context to store parameters
+ * \param N        RSA modulus, or NULL
+ * \param P        First prime factor of N, or NULL
+ * \param Q        Second prime factor of N, or NULL
+ * \param D        Private exponent, or NULL
+ * \param E        Public exponent, or NULL
+ *
+ * \note           This function can be called multiple times for successive
+ *                 imports if the parameters are not simultaneously present.
+ *                 Any sequence of calls to this function should be followed
+ *                 by a call to \c mbedtls_rsa_complete which will check
+ *                 and complete the provided information to a ready-for-use
+ *                 public or private RSA key.
+ *
+ * \note           See the documentation of \c mbedtls_rsa_complete for more
+ *                 information on which parameters are necessary to setup
+ *                 a private or public RSA key.
+ *
+ * \note           The imported parameters are copied and need not be preserved
+ *                 for the lifetime of the RSA context being set up.
+ *
+ * \return         0 if successful, non-zero error code on failure.
+ */
+int mbedtls_rsa_import( mbedtls_rsa_context *ctx,
+                        const mbedtls_mpi *N,
+                        const mbedtls_mpi *P, const mbedtls_mpi *Q,
+                        const mbedtls_mpi *D, const mbedtls_mpi *E );
+
+/**
+ * \brief          Import core RSA parameters in raw big-endian
+ *                 binary format into an RSA context
+ *
+ * \param ctx      Initialized RSA context to store parameters
+ * \param N        RSA modulus, or NULL
+ * \param N_len    Byte length of N, ignored if N == NULL
+ * \param P        First prime factor of N, or NULL
+ * \param P_len    Byte length of P, ignored if P == NULL
+ * \param Q        Second prime factor of N, or NULL
+ * \param Q_len    Byte length of Q, ignored if Q == NULL
+ * \param D        Private exponent, or NULL
+ * \param D_len    Byte length of D, ignored if D == NULL
+ * \param E        Public exponent, or NULL
+ * \param E_len    Byte length of E, ignored if E == NULL
+ *
+ * \note           This function can be called multiple times for successive
+ *                 imports if the parameters are not simultaneously present.
+ *                 Any sequence of calls to this function should be followed
+ *                 by a call to \c mbedtls_rsa_complete which will check
+ *                 and complete the provided information to a ready-for-use
+ *                 public or private RSA key.
+ *
+ * \note           See the documentation of \c mbedtls_rsa_complete for more
+ *                 information on which parameters are necessary to setup
+ *                 a private or public RSA key.
+ *
+ * \note           The imported parameters are copied and need not be preserved
+ *                 for the lifetime of the RSA context being set up.
+ *
+ * \return         0 if successful, non-zero error code on failure.
+ */
+int mbedtls_rsa_import_raw( mbedtls_rsa_context *ctx,
+                            unsigned char const *N, size_t N_len,
+                            unsigned char const *P, size_t P_len,
+                            unsigned char const *Q, size_t Q_len,
+                            unsigned char const *D, size_t D_len,
+                            unsigned char const *E, size_t E_len );
+
+/**
+ * \brief          Attempt to complete an RSA context from
+ *                 a set of imported core parameters.
+ *
+ * \param ctx      Initialized RSA context to store parameters
+ *
+ * \note
+ *                 - To setup an RSA public key, precisely N and E
+ *                   must have been imported.
+ *
+ *                 - To setup an RSA private key, enough information must be
+ *                   present for the other parameters to be derivable.
+ *
+ *                   The default implementation supports the following:
+ *                     - Derive P, Q from N, D, E
+ *                     - Derive N, D from P, Q, E.
+ *
+ *                 - Alternative implementations need not support these
+ *                   and may return \c MBEDTLS_ERR_RSA_BAD_INPUT_DATA instead.
+ *
+ * \return
+ *                 - 0 if successful. In this case, it is guaranteed
+ *                   that the RSA context can be used for RSA operations
+ *                   without the risk of failure or crash.
+ *                 - \c MBEDTLS_ERR_RSA_BAD_INPUT_DATA if the attempted
+ *                   derivations failed.
+ *
+ * \warning        This function need not perform consistency checks
+ *                 for the imported parameters! In particular, parameters that
+ *                 are not needed by the implementation may be silently discarded
+ *                 and left unchecked. For the purpose of checking the consistency
+ *                 of the key material, see \c mbedtls_rsa_check_privkey.
+ *
+ */
+int mbedtls_rsa_complete( mbedtls_rsa_context *ctx );
+
+/**
+ * \brief          Export core parameters of an RSA key
+ *
+ * \param ctx      Initialized RSA context
+ * \param N        MPI to hold the RSA modulus, or NULL
+ * \param P        MPI to hold the first prime factor of N, or NULL
+ * \param Q        MPI to hold the second prime factor of N, or NULL
+ * \param D        MPI to hold the private exponent, or NULL
+ * \param E        MPI to hold the public exponent, or NULL
+ *
+ * \return
+ *                 - 0 if successful. In this case, the non-NULL buffers
+ *                   pointed to by N, P, Q, D, E are fully written, with
+ *                   additional unused space filled leading by 0-bytes.
+ *                 - Non-zero return code otherwise. In particular, if
+ *                   exporting the requested parameters
+ *                   cannot be done because of a lack of functionality
+ *                   or because of security policies, the error code
+ *                   \c MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION is returned.
+ *                   In this case, the RSA context stays intact and can
+ *                   be continued to be used.
+ *
+ * \note           Reasons for returning \c MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION
+ *                 would be the following: Firstly, it might be that an
+ *                 alternative RSA implementation is in use which stores
+ *                 the key externally, and which either cannot or should not
+ *                 export it into RAM. Alternatively, an implementation
+ *                 (regardless of SW or HW) might not support deducing e.g.
+ *                 P, Q from N, D, E if the former are not part of the
+ *                 implementation.
+ *
+ */
+int mbedtls_rsa_export( const mbedtls_rsa_context *ctx,
+                        mbedtls_mpi *N, mbedtls_mpi *P, mbedtls_mpi *Q,
+                        mbedtls_mpi *D, mbedtls_mpi *E );
+
+/**
+ * \brief          Export core parameters of an RSA key
+ *                 in raw big-endian binary format
+ *
+ * \param ctx      Initialized RSA context
+ * \param N        Byte array to store the RSA modulus, or NULL
+ * \param N_len    Size of buffer for modulus
+ * \param P        Byte array to hold the first prime factor of N, or NULL
+ * \param P_len    Size of buffer for first prime factor
+ * \param Q        Byte array to hold the second prime factor of N, or NULL
+ * \param Q_len    Size of buffer for second prime factor
+ * \param D        Byte array to hold the private exponent, or NULL
+ * \param D_len    Size of buffer for private exponent
+ * \param E        Byte array to hold the public exponent, or NULL
+ * \param E_len    Size of buffer for public exponent
+ *
+ * \note           The length fields are ignored if the corresponding
+ *                 buffer pointers are NULL.
+ *
+ * \return
+ *                 - 0 if successful. In this case, the non-NULL buffers
+ *                   pointed to by N, P, Q, D, E are fully written, with
+ *                   additional unused space filled leading by 0-bytes.
+ *                 - Non-zero return code otherwise. In particular, if
+ *                   exporting the requested parameters
+ *                   cannot be done because of a lack of functionality
+ *                   or because of security policies, the error code
+ *                   \c MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION is returned.
+ *                   In this case, the RSA context stays intact and can
+ *                   be continued to be used.
+ *
+ * \note           Reasons for returning \c MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION
+ *                 would be the following: Firstly, it might be that an
+ *                 alternative RSA implementation is in use which stores
+ *                 the key externally, and which either cannot or should not
+ *                 export it into RAM. Alternatively, an implementation
+ *                 (regardless of SW or HW) might not support deducing e.g.
+ *                 P, Q from N, D, E if the former are not part of the
+ *                 implementation.
+ *
+ *
+ */
+int mbedtls_rsa_export_raw( const mbedtls_rsa_context *ctx,
+                            unsigned char *N, size_t N_len,
+                            unsigned char *P, size_t P_len,
+                            unsigned char *Q, size_t Q_len,
+                            unsigned char *D, size_t D_len,
+                            unsigned char *E, size_t E_len );
+
+/**
+ * \brief          Export CRT parameters of a private RSA key
+ *
+ * \param ctx      Initialized RSA context
+ * \param DP       MPI to hold D modulo P-1, or NULL
+ * \param DQ       MPI to hold D modulo Q-1, or NULL
+ * \param QP       MPI to hold modular inverse of Q modulo P, or NULL
+ *
+ * \return         0 if successful, non-zero error code otherwise.
+ *
+ * \note           Alternative RSA implementations not using CRT-parameters
+ *                 internally can implement this function using based on
+ *                 \c mbedtls_rsa_deduce_opt.
+ *
+ */
+int mbedtls_rsa_export_crt( const mbedtls_rsa_context *ctx,
+                            mbedtls_mpi *DP, mbedtls_mpi *DQ, mbedtls_mpi *QP );
 
 /**
  * \brief          Set padding for an already initialized RSA context
  *                 See \c mbedtls_rsa_init() for details.
  *
  * \param ctx      RSA context to be set
- * \param padding  MBEDTLS_RSA_PKCS_V15 or MBEDTLS_RSA_PKCS_V21
+ * \param padding  \c MBEDTLS_RSA_PKCS_V15 or \c MBEDTLS_RSA_PKCS_V21
- * \param hash_id  MBEDTLS_RSA_PKCS_V21 hash identifier
+ * \param hash_id  \c MBEDTLS_RSA_PKCS_V21 hash identifier
  */
-void mbedtls_rsa_set_padding( mbedtls_rsa_context *ctx, int padding, int hash_id);
+void mbedtls_rsa_set_padding( mbedtls_rsa_context *ctx, int padding,
+                              int hash_id);
+
+/**
+ * \brief          Get length of RSA modulus in bytes
+ *
+ * \param ctx      Initialized RSA context
+ *
+ * \return         Length of RSA modulus, in bytes.
+ *
+ */
+size_t mbedtls_rsa_get_len( const mbedtls_rsa_context *ctx );
 
 /**
  * \brief          Generate an RSA keypair
@@ -161,28 +392,61 @@ void mbedtls_rsa_set_padding( mbedtls_rsa_context *ctx, int padding, int hash_id
  * \note           mbedtls_rsa_init() must be called beforehand to setup
  *                 the RSA context.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  */
 int mbedtls_rsa_gen_key( mbedtls_rsa_context *ctx,
-                 int (*f_rng)(void *, unsigned char *, size_t),
+                         int (*f_rng)(void *, unsigned char *, size_t),
-                 void *p_rng,
+                         void *p_rng,
-                 unsigned int nbits, int exponent );
+                         unsigned int nbits, int exponent );
 
 /**
- * \brief          Check a public RSA key
+ * \brief          Check if a context contains (at least) an RSA public key
  *
  * \param ctx      RSA context to be checked
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code.
+ *                 On success, it is guaranteed that enough information is
+ *                 present to perform an RSA public key operation
+ *                 \c mbedtls_rsa_public.
+ *
  */
 int mbedtls_rsa_check_pubkey( const mbedtls_rsa_context *ctx );
 
 /**
- * \brief          Check a private RSA key
+ * \brief      Check if a context contains an RSA private key
+ *             and perform basic consistency checks.
  *
- * \param ctx      RSA context to be checked
+ * \param ctx  RSA context to be checked
+ *
+ * \return     0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code.
+ *
+ * \note       The consistency checks performed by this function not only
+ *             ensure that \c mbedtls_rsa_private can be called successfully
+ *             on the given context, but that the various parameters are
+ *             mutually consistent with high probability, in the sense that
+ *             \c mbedtls_rsa_public and \c mbedtls_rsa_private are inverses.
+ *
+ * \warning    This function should catch accidental misconfigurations
+ *             like swapping of parameters, but it cannot establish full
+ *             trust in neither the quality nor the consistency of the key
+ *             material that was used to setup the given RSA context:
+ *             - Regarding consistency, note (see \c mbedtls_rsa_complete)
+ *               that imported parameters irrelevant for the implementation
+ *               might be silently dropped, in which case the present
+ *               function doesn't have access to and hence cannot check them.
+ *               If you want to check the consistency of the entire
+ *               content of, say, an PKCS1-encoded RSA private key, you
+ *               should use \c mbedtls_rsa_validate_params before setting
+ *               up the RSA context.
+ *               Further, if the implementation performs empirical checks,
+ *               these checks will substantiate but not guarantee consistency.
+ *             - Regarding quality, this function is not expected to perform
+ *               extended quality assessments like checking that the prime
+ *               factors are safe. Further, it is the user's responsibility to
+ *               ensure trustworthiness of the source of his RSA parameters,
+ *               a question going beyond what's effectively checkable
+ *               by the library.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
  */
 int mbedtls_rsa_check_privkey( const mbedtls_rsa_context *ctx );
 
@@ -193,9 +457,10 @@ int mbedtls_rsa_check_privkey( const mbedtls_rsa_context *ctx );
  * \param pub      RSA context holding the public key
  * \param prv      RSA context holding the private key
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  */
-int mbedtls_rsa_check_pub_priv( const mbedtls_rsa_context *pub, const mbedtls_rsa_context *prv );
+int mbedtls_rsa_check_pub_priv( const mbedtls_rsa_context *pub,
+                                const mbedtls_rsa_context *prv );
 
 /**
  * \brief          Do an RSA public key operation
@@ -204,7 +469,7 @@ int mbedtls_rsa_check_pub_priv( const mbedtls_rsa_context *pub, const mbedtls_rs
  * \param input    input buffer
  * \param output   output buffer
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  *
  * \note           This function does NOT take care of message
  *                 padding. Also, be sure to set input[0] = 0 or ensure that
@@ -226,7 +491,7 @@ int mbedtls_rsa_public( mbedtls_rsa_context *ctx,
  * \param input    input buffer
  * \param output   output buffer
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  *
  * \note           The input and output buffers must be large
  *                 enough (eg. 128 bytes if RSA-1024 is used).
@@ -244,9 +509,9 @@ int mbedtls_rsa_private( mbedtls_rsa_context *ctx,
  *
  * \param ctx      RSA context
  * \param f_rng    RNG function (Needed for padding and PKCS#1 v2.1 encoding
- *                               and MBEDTLS_RSA_PRIVATE)
+ *                               and \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
  * \param ilen     contains the plaintext length
  * \param input    buffer holding the data to be encrypted
  * \param output   buffer that will hold the ciphertext
@@ -260,7 +525,7 @@ int mbedtls_rsa_private( mbedtls_rsa_context *ctx,
  *                 mode being set to MBEDTLS_RSA_PRIVATE and may instead
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  *
  * \note           The output buffer must be as large as the size
  *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
@@ -276,9 +541,9 @@ int mbedtls_rsa_pkcs1_encrypt( mbedtls_rsa_context *ctx,
  * \brief          Perform a PKCS#1 v1.5 encryption (RSAES-PKCS1-v1_5-ENCRYPT)
  *
  * \param ctx      RSA context
- * \param f_rng    RNG function (Needed for padding and MBEDTLS_RSA_PRIVATE)
+ * \param f_rng    RNG function (Needed for padding and \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
  * \param ilen     contains the plaintext length
  * \param input    buffer holding the data to be encrypted
  * \param output   buffer that will hold the ciphertext
@@ -292,7 +557,7 @@ int mbedtls_rsa_pkcs1_encrypt( mbedtls_rsa_context *ctx,
  *                 mode being set to MBEDTLS_RSA_PRIVATE and may instead
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  *
  * \note           The output buffer must be as large as the size
  *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
@@ -309,9 +574,9 @@ int mbedtls_rsa_rsaes_pkcs1_v15_encrypt( mbedtls_rsa_context *ctx,
  *
  * \param ctx      RSA context
  * \param f_rng    RNG function (Needed for padding and PKCS#1 v2.1 encoding
- *                               and MBEDTLS_RSA_PRIVATE)
+ *                               and \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
  * \param label    buffer holding the custom label to use
  * \param label_len contains the label length
  * \param ilen     contains the plaintext length
@@ -327,7 +592,7 @@ int mbedtls_rsa_rsaes_pkcs1_v15_encrypt( mbedtls_rsa_context *ctx,
  *                 mode being set to MBEDTLS_RSA_PRIVATE and may instead
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  *
  * \note           The output buffer must be as large as the size
  *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
@@ -347,9 +612,9 @@ int mbedtls_rsa_rsaes_oaep_encrypt( mbedtls_rsa_context *ctx,
  *                 the message padding
  *
  * \param ctx      RSA context
- * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
+ * \param f_rng    RNG function (Only needed for \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
  * \param olen     will contain the plaintext length
  * \param input    buffer holding the encrypted data
  * \param output   buffer that will hold the plaintext
@@ -364,17 +629,17 @@ int mbedtls_rsa_rsaes_oaep_encrypt( mbedtls_rsa_context *ctx,
  *                 mode being set to MBEDTLS_RSA_PUBLIC and may instead
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  *
  * \note           The output buffer length \c output_max_len should be
- *                 as large as the size ctx->len of ctx->N (eg. 128 bytes
+ *                 as large as the size \c ctx->len of \c ctx->N (eg. 128 bytes
  *                 if RSA-1024 is used) to be able to hold an arbitrary
  *                 decrypted message. If it is not large enough to hold
  *                 the decryption of the particular ciphertext provided,
- *                 the function will return MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE.
+ *                 the function will return \c MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE.
  *
  * \note           The input buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
  */
 int mbedtls_rsa_pkcs1_decrypt( mbedtls_rsa_context *ctx,
                        int (*f_rng)(void *, unsigned char *, size_t),
@@ -388,9 +653,9 @@ int mbedtls_rsa_pkcs1_decrypt( mbedtls_rsa_context *ctx,
  * \brief          Perform a PKCS#1 v1.5 decryption (RSAES-PKCS1-v1_5-DECRYPT)
  *
  * \param ctx      RSA context
- * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
+ * \param f_rng    RNG function (Only needed for \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
  * \param olen     will contain the plaintext length
  * \param input    buffer holding the encrypted data
  * \param output   buffer that will hold the plaintext
@@ -405,17 +670,17 @@ int mbedtls_rsa_pkcs1_decrypt( mbedtls_rsa_context *ctx,
  *                 mode being set to MBEDTLS_RSA_PUBLIC and may instead
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  *
  * \note           The output buffer length \c output_max_len should be
- *                 as large as the size ctx->len of ctx->N (eg. 128 bytes
+ *                 as large as the size \c ctx->len of \c ctx->N (eg. 128 bytes
  *                 if RSA-1024 is used) to be able to hold an arbitrary
  *                 decrypted message. If it is not large enough to hold
  *                 the decryption of the particular ciphertext provided,
- *                 the function will return MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE.
+ *                 the function will return \c MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE.
  *
  * \note           The input buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
  */
 int mbedtls_rsa_rsaes_pkcs1_v15_decrypt( mbedtls_rsa_context *ctx,
                                  int (*f_rng)(void *, unsigned char *, size_t),
@@ -429,9 +694,9 @@ int mbedtls_rsa_rsaes_pkcs1_v15_decrypt( mbedtls_rsa_context *ctx,
  * \brief          Perform a PKCS#1 v2.1 OAEP decryption (RSAES-OAEP-DECRYPT)
  *
  * \param ctx      RSA context
- * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
+ * \param f_rng    RNG function (Only needed for \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
  * \param label    buffer holding the custom label to use
  * \param label_len contains the label length
  * \param olen     will contain the plaintext length
@@ -448,17 +713,18 @@ int mbedtls_rsa_rsaes_pkcs1_v15_decrypt( mbedtls_rsa_context *ctx,
  *                 mode being set to MBEDTLS_RSA_PUBLIC and may instead
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_RSA_XXX error code
+ * \return         0 if successful, or an \c MBEDTLS_ERR_RSA_XXX error code
  *
  * \note           The output buffer length \c output_max_len should be
- *                 as large as the size ctx->len of ctx->N (eg. 128 bytes
+ *                 as large as the size \c ctx->len of \c ctx->N (eg. 128 bytes
  *                 if RSA-1024 is used) to be able to hold an arbitrary
  *                 decrypted message. If it is not large enough to hold
  *                 the decryption of the particular ciphertext provided,
- *                 the function will return MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE.
+ *                 the function will return \c MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE.
  *
  * \note           The input buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *
  */
 int mbedtls_rsa_rsaes_oaep_decrypt( mbedtls_rsa_context *ctx,
                             int (*f_rng)(void *, unsigned char *, size_t),
@@ -477,11 +743,12 @@ int mbedtls_rsa_rsaes_oaep_decrypt( mbedtls_rsa_context *ctx,
  *
  * \param ctx      RSA context
  * \param f_rng    RNG function (Needed for PKCS#1 v2.1 encoding and for
- *                               MBEDTLS_RSA_PRIVATE)
+ *                               \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
- * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
+ * \param md_alg   a \c MBEDTLS_MD_XXX (use \c MBEDTLS_MD_NONE for
- * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
+ *                 signing raw data)
+ * \param hashlen  message digest length (for \c MBEDTLS_MD_NONE only)
  * \param hash     buffer holding the message digest
  * \param sig      buffer that will hold the ciphertext
  *
@@ -495,13 +762,14 @@ int mbedtls_rsa_rsaes_oaep_decrypt( mbedtls_rsa_context *ctx,
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
  * \return         0 if the signing operation was successful,
- *                 or an MBEDTLS_ERR_RSA_XXX error code
+ *                 or an \c MBEDTLS_ERR_RSA_XXX error code
  *
- * \note           The "sig" buffer must be as large as the size
+ * \note           The \c sig buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
  *
  * \note           In case of PKCS#1 v2.1 encoding, see comments on
- * \note           \c mbedtls_rsa_rsassa_pss_sign() for details on md_alg and hash_id.
+ *                 \c mbedtls_rsa_rsassa_pss_sign() for details on
+ *                 \c md_alg and \c hash_id.
  */
 int mbedtls_rsa_pkcs1_sign( mbedtls_rsa_context *ctx,
                     int (*f_rng)(void *, unsigned char *, size_t),
@@ -516,11 +784,12 @@ int mbedtls_rsa_pkcs1_sign( mbedtls_rsa_context *ctx,
  * \brief          Perform a PKCS#1 v1.5 signature (RSASSA-PKCS1-v1_5-SIGN)
  *
  * \param ctx      RSA context
- * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
+ * \param f_rng    RNG function (Only needed for \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
- * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
+ * \param md_alg   a \c MBEDTLS_MD_XXX (use \c MBEDTLS_MD_NONE
- * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
+ *                 for signing raw data)
+ * \param hashlen  message digest length (for \c MBEDTLS_MD_NONE only)
  * \param hash     buffer holding the message digest
  * \param sig      buffer that will hold the ciphertext
  *
@@ -534,10 +803,10 @@ int mbedtls_rsa_pkcs1_sign( mbedtls_rsa_context *ctx,
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
  * \return         0 if the signing operation was successful,
- *                 or an MBEDTLS_ERR_RSA_XXX error code
+ *                 or an \c MBEDTLS_ERR_RSA_XXX error code
  *
- * \note           The "sig" buffer must be as large as the size
+ * \note           The \c sig buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
  */
 int mbedtls_rsa_rsassa_pkcs1_v15_sign( mbedtls_rsa_context *ctx,
                                int (*f_rng)(void *, unsigned char *, size_t),
@@ -553,11 +822,12 @@ int mbedtls_rsa_rsassa_pkcs1_v15_sign( mbedtls_rsa_context *ctx,
  *
  * \param ctx      RSA context
  * \param f_rng    RNG function (Needed for PKCS#1 v2.1 encoding and for
- *                               MBEDTLS_RSA_PRIVATE)
+ *                               \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
- * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
+ * \param md_alg   a \c MBEDTLS_MD_XXX (use \c MBEDTLS_MD_NONE
- * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
+ *                 for signing raw data)
+ * \param hashlen  message digest length (for \c MBEDTLS_MD_NONE only)
  * \param hash     buffer holding the message digest
  * \param sig      buffer that will hold the ciphertext
  *
@@ -571,13 +841,13 @@ int mbedtls_rsa_rsassa_pkcs1_v15_sign( mbedtls_rsa_context *ctx,
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
  * \return         0 if the signing operation was successful,
- *                 or an MBEDTLS_ERR_RSA_XXX error code
+ *                 or an \c MBEDTLS_ERR_RSA_XXX error code
  *
- * \note           The "sig" buffer must be as large as the size
+ * \note           The \c sig buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
  *
- * \note           The hash_id in the RSA context is the one used for the
+ * \note           The \c hash_id in the RSA context is the one used for the
- *                 encoding. md_alg in the function call is the type of hash
+ *                 encoding. \c md_alg in the function call is the type of hash
  *                 that is encoded. According to RFC 3447 it is advised to
  *                 keep both hashes the same.
  */
@@ -596,11 +866,11 @@ int mbedtls_rsa_rsassa_pss_sign( mbedtls_rsa_context *ctx,
  *                 the message digest
  *
  * \param ctx      points to an RSA public key
- * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
+ * \param f_rng    RNG function (Only needed for \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
- * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
+ * \param md_alg   a \c MBEDTLS_MD_XXX (use \c MBEDTLS_MD_NONE for signing raw data)
- * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
+ * \param hashlen  message digest length (for \c MBEDTLS_MD_NONE only)
  * \param hash     buffer holding the message digest
  * \param sig      buffer holding the ciphertext
  *
@@ -614,10 +884,10 @@ int mbedtls_rsa_rsassa_pss_sign( mbedtls_rsa_context *ctx,
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
  * \return         0 if the verify operation was successful,
- *                 or an MBEDTLS_ERR_RSA_XXX error code
+ *                 or an \c MBEDTLS_ERR_RSA_XXX error code
  *
- * \note           The "sig" buffer must be as large as the size
+ * \note           The \c sig buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
  *
  * \note           In case of PKCS#1 v2.1 encoding, see comments on
  *                 \c mbedtls_rsa_rsassa_pss_verify() about md_alg and hash_id.
@@ -635,11 +905,12 @@ int mbedtls_rsa_pkcs1_verify( mbedtls_rsa_context *ctx,
  * \brief          Perform a PKCS#1 v1.5 verification (RSASSA-PKCS1-v1_5-VERIFY)
  *
  * \param ctx      points to an RSA public key
- * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
+ * \param f_rng    RNG function (Only needed for \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
- * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
+ * \param md_alg   a \c MBEDTLS_MD_XXX (use \c MBEDTLS_MD_NONE
- * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
+ *                 for signing raw data)
+ * \param hashlen  message digest length (for \c MBEDTLS_MD_NONE only)
  * \param hash     buffer holding the message digest
  * \param sig      buffer holding the ciphertext
  *
@@ -653,10 +924,10 @@ int mbedtls_rsa_pkcs1_verify( mbedtls_rsa_context *ctx,
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
  * \return         0 if the verify operation was successful,
- *                 or an MBEDTLS_ERR_RSA_XXX error code
+ *                 or an \c MBEDTLS_ERR_RSA_XXX error code
  *
- * \note           The "sig" buffer must be as large as the size
+ * \note           The \c sig buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
  */
 int mbedtls_rsa_rsassa_pkcs1_v15_verify( mbedtls_rsa_context *ctx,
                                  int (*f_rng)(void *, unsigned char *, size_t),
@@ -672,11 +943,11 @@ int mbedtls_rsa_rsassa_pkcs1_v15_verify( mbedtls_rsa_context *ctx,
  *                 (This is the "simple" version.)
  *
  * \param ctx      points to an RSA public key
- * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
+ * \param f_rng    RNG function (Only needed for \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
- * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
+ * \param md_alg   a \c MBEDTLS_MD_XXX (use \c MBEDTLS_MD_NONE for signing raw data)
- * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
+ * \param hashlen  message digest length (for \c MBEDTLS_MD_NONE only)
  * \param hash     buffer holding the message digest
  * \param sig      buffer holding the ciphertext
  *
@@ -690,16 +961,16 @@ int mbedtls_rsa_rsassa_pkcs1_v15_verify( mbedtls_rsa_context *ctx,
  *                 return MBEDTLS_ERR_RSA_UNSUPPORTED_OPERATION.
  *
  * \return         0 if the verify operation was successful,
- *                 or an MBEDTLS_ERR_RSA_XXX error code
+ *                 or an \c MBEDTLS_ERR_RSA_XXX error code
  *
- * \note           The "sig" buffer must be as large as the size
+ * \note           The \c sig buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
  *
- * \note           The hash_id in the RSA context is the one used for the
+ * \note           The \c hash_id in the RSA context is the one used for the
- *                 verification. md_alg in the function call is the type of
+ *                 verification. \c md_alg in the function call is the type of
  *                 hash that is verified. According to RFC 3447 it is advised to
- *                 keep both hashes the same. If hash_id in the RSA context is
+ *                 keep both hashes the same. If \c hash_id in the RSA context is
- *                 unset, the md_alg from the function call is used.
+ *                 unset, the \c md_alg from the function call is used.
  */
 int mbedtls_rsa_rsassa_pss_verify( mbedtls_rsa_context *ctx,
                            int (*f_rng)(void *, unsigned char *, size_t),
@@ -715,24 +986,24 @@ int mbedtls_rsa_rsassa_pss_verify( mbedtls_rsa_context *ctx,
  *                 (This is the version with "full" options.)
  *
  * \param ctx      points to an RSA public key
- * \param f_rng    RNG function (Only needed for MBEDTLS_RSA_PRIVATE)
+ * \param f_rng    RNG function (Only needed for \c MBEDTLS_RSA_PRIVATE)
  * \param p_rng    RNG parameter
- * \param mode     MBEDTLS_RSA_PUBLIC or MBEDTLS_RSA_PRIVATE
+ * \param mode     \c MBEDTLS_RSA_PUBLIC or \c MBEDTLS_RSA_PRIVATE
- * \param md_alg   a MBEDTLS_MD_XXX (use MBEDTLS_MD_NONE for signing raw data)
+ * \param md_alg   a \c MBEDTLS_MD_XXX (use \c MBEDTLS_MD_NONE for signing raw data)
- * \param hashlen  message digest length (for MBEDTLS_MD_NONE only)
+ * \param hashlen  message digest length (for \c MBEDTLS_MD_NONE only)
  * \param hash     buffer holding the message digest
  * \param mgf1_hash_id message digest used for mask generation
  * \param expected_salt_len Length of the salt used in padding, use
- *                 MBEDTLS_RSA_SALT_LEN_ANY to accept any salt length
+ *                 \c MBEDTLS_RSA_SALT_LEN_ANY to accept any salt length
  * \param sig      buffer holding the ciphertext
  *
  * \return         0 if the verify operation was successful,
- *                 or an MBEDTLS_ERR_RSA_XXX error code
+ *                 or an \c MBEDTLS_ERR_RSA_XXX error code
  *
- * \note           The "sig" buffer must be as large as the size
+ * \note           The \c sig buffer must be as large as the size
- *                 of ctx->N (eg. 128 bytes if RSA-1024 is used).
+ *                 of \c ctx->N (eg. 128 bytes if RSA-1024 is used).
  *
- * \note           The hash_id in the RSA context is ignored.
+ * \note           The \c hash_id in the RSA context is ignored.
  */
 int mbedtls_rsa_rsassa_pss_verify_ext( mbedtls_rsa_context *ctx,
                                int (*f_rng)(void *, unsigned char *, size_t),
@@ -752,7 +1023,7 @@ int mbedtls_rsa_rsassa_pss_verify_ext( mbedtls_rsa_context *ctx,
  * \param src      Source context
  *
  * \return         0 on success,
- *                 MBEDTLS_ERR_MPI_ALLOC_FAILED on memory allocation failure
+ *                 \c MBEDTLS_ERR_MPI_ALLOC_FAILED on memory allocation failure
  */
 int mbedtls_rsa_copy( mbedtls_rsa_context *dst, const mbedtls_rsa_context *src );
 
@@ -763,6 +1034,18 @@ int mbedtls_rsa_copy( mbedtls_rsa_context *dst, const mbedtls_rsa_context *src )
  */
 void mbedtls_rsa_free( mbedtls_rsa_context *ctx );
 
+#ifdef __cplusplus
+}
+#endif
+
+#else  /* MBEDTLS_RSA_ALT */
+#include "rsa_alt.h"
+#endif /* MBEDTLS_RSA_ALT */
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
 /**
  * \brief          Checkup routine
  *
@@ -774,6 +1057,4 @@ int mbedtls_rsa_self_test( int verbose );
 }
 #endif
 
-#endif /* MBEDTLS_RSA_C */
-
 #endif /* rsa.h */

include/mbedtls/rsa_internal.h

@@ -0,0 +1,215 @@
+/**
+ * \file rsa_internal.h
+ *
+ * \brief Context-independent RSA helper functions
+ *
+ *  Copyright (C) 2006-2017, ARM Limited, All Rights Reserved
+ *  SPDX-License-Identifier: Apache-2.0
+ *
+ *  Licensed under the Apache License, Version 2.0 (the "License"); you may
+ *  not use this file except in compliance with the License.
+ *  You may obtain a copy of the License at
+ *
+ *  http://www.apache.org/licenses/LICENSE-2.0
+ *
+ *  Unless required by applicable law or agreed to in writing, software
+ *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+ *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ *  See the License for the specific language governing permissions and
+ *  limitations under the License.
+ *
+ *  This file is part of mbed TLS (https://tls.mbed.org)
+ *
+ *
+ *  This file declares some RSA-related helper functions useful when
+ *  implementing the RSA interface. They are public and provided in a
+ *  separate compilation unit in order to make it easy for designers of
+ *  alternative RSA implementations to use them in their code, as it is
+ *  conceived that the functionality they provide will be necessary
+ *  for most complete implementations.
+ *
+ *  End-users of Mbed TLS not intending to re-implement the RSA functionality
+ *  are not expected to get into the need of making use of these functions directly,
+ *  but instead should be able to use the functions declared in rsa.h.
+ *
+ *  There are two classes of helper functions:
+ *  (1) Parameter-generating helpers. These are:
+ *      - mbedtls_rsa_deduce_primes
+ *      - mbedtls_rsa_deduce_private_exponent
+ *      - mbedtls_rsa_deduce_crt
+ *       Each of these functions takes a set of core RSA parameters
+ *       and generates some other, or CRT related parameters.
+ *  (2) Parameter-checking helpers. These are:
+ *      - mbedtls_rsa_validate_params
+ *      - mbedtls_rsa_validate_crt
+ *      They take a set of core or CRT related RSA parameters
+ *      and check their validity.
+ *
+ */
+
+#ifndef MBEDTLS_RSA_INTERNAL_H
+#define MBEDTLS_RSA_INTERNAL_H
+
+#if !defined(MBEDTLS_CONFIG_FILE)
+#include "config.h"
+#else
+#include MBEDTLS_CONFIG_FILE
+#endif
+
+#include "bignum.h"
+
+#ifdef __cplusplus
+extern "C" {
+#endif
+
+
+/**
+ * \brief          Compute RSA prime moduli P, Q from public modulus N=PQ
+ *                 and a pair of private and public key.
+ *
+ * \note           This is a 'static' helper function not operating on
+ *                 an RSA context. Alternative implementations need not
+ *                 overwrite it.
+ *
+ * \param N        RSA modulus N = PQ, with P, Q to be found
+ * \param E        RSA public exponent
+ * \param D        RSA private exponent
+ * \param P        Pointer to MPI holding first prime factor of N on success
+ * \param Q        Pointer to MPI holding second prime factor of N on success
+ *
+ * \return
+ *                 - 0 if successful. In this case, P and Q constitute a
+ *                   factorization of N.
+ *                 - A non-zero error code otherwise.
+ *
+ * \note           It is neither checked that P, Q are prime nor that
+ *                 D, E are modular inverses wrt. P-1 and Q-1. For that,
+ *                 use the helper function \c mbedtls_rsa_validate_params.
+ *
+ */
+int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N, mbedtls_mpi const *E,
+                               mbedtls_mpi const *D,
+                               mbedtls_mpi *P, mbedtls_mpi *Q );
+
+/**
+ * \brief          Compute RSA private exponent from
+ *                 prime moduli and public key.
+ *
+ * \note           This is a 'static' helper function not operating on
+ *                 an RSA context. Alternative implementations need not
+ *                 overwrite it.
+ *
+ * \param P        First prime factor of RSA modulus
+ * \param Q        Second prime factor of RSA modulus
+ * \param E        RSA public exponent
+ * \param D        Pointer to MPI holding the private exponent on success.
+ *
+ * \return
+ *                 - 0 if successful. In this case, D is set to a simultaneous
+ *                   modular inverse of E modulo both P-1 and Q-1.
+ *                 - A non-zero error code otherwise.
+ *
+ * \note           This function does not check whether P and Q are primes.
+ *
+ */
+int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P,
+                                         mbedtls_mpi const *Q,
+                                         mbedtls_mpi const *E,
+                                         mbedtls_mpi *D );
+
+
+/**
+ * \brief          Generate RSA-CRT parameters
+ *
+ * \note           This is a 'static' helper function not operating on
+ *                 an RSA context. Alternative implementations need not
+ *                 overwrite it.
+ *
+ * \param P        First prime factor of N
+ * \param Q        Second prime factor of N
+ * \param D        RSA private exponent
+ * \param DP       Output variable for D modulo P-1
+ * \param DQ       Output variable for D modulo Q-1
+ * \param QP       Output variable for the modular inverse of Q modulo P.
+ *
+ * \return         0 on success, non-zero error code otherwise.
+ *
+ * \note           This function does not check whether P, Q are
+ *                 prime and whether D is a valid private exponent.
+ *
+ */
+int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
+                            const mbedtls_mpi *D, mbedtls_mpi *DP,
+                            mbedtls_mpi *DQ, mbedtls_mpi *QP );
+
+
+/**
+ * \brief          Check validity of core RSA parameters
+ *
+ * \note           This is a 'static' helper function not operating on
+ *                 an RSA context. Alternative implementations need not
+ *                 overwrite it.
+ *
+ * \param N        RSA modulus N = PQ
+ * \param P        First prime factor of N
+ * \param Q        Second prime factor of N
+ * \param D        RSA private exponent
+ * \param E        RSA public exponent
+ * \param f_rng    PRNG to be used for primality check, or NULL
+ * \param p_rng    PRNG context for f_rng, or NULL
+ *
+ * \return
+ *                 - 0 if the following conditions are satisfied
+ *                   if all relevant parameters are provided:
+ *                    - P prime if f_rng != NULL (%)
+ *                    - Q prime if f_rng != NULL (%)
+ *                    - 1 < N = P * Q
+ *                    - 1 < D, E < N
+ *                    - D and E are modular inverses modulo P-1 and Q-1
+ *                   (%) This is only done if MBEDTLS_GENPRIME is defined.
+ *                 - A non-zero error code otherwise.
+ *
+ * \note           The function can be used with a restricted set of arguments
+ *                 to perform specific checks only. E.g., calling it with
+ *                 (-,P,-,-,-) and a PRNG amounts to a primality check for P.
+ */
+int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P,
+                                 const mbedtls_mpi *Q, const mbedtls_mpi *D,
+                                 const mbedtls_mpi *E,
+                                 int (*f_rng)(void *, unsigned char *, size_t),
+                                 void *p_rng );
+
+/**
+ * \brief          Check validity of RSA CRT parameters
+ *
+ * \note           This is a 'static' helper function not operating on
+ *                 an RSA context. Alternative implementations need not
+ *                 overwrite it.
+ *
+ * \param P        First prime factor of RSA modulus
+ * \param Q        Second prime factor of RSA modulus
+ * \param D        RSA private exponent
+ * \param DP       MPI to check for D modulo P-1
+ * \param DQ       MPI to check for D modulo P-1
+ * \param QP       MPI to check for the modular inverse of Q modulo P.
+ *
+ * \return
+ *                 - 0 if the following conditions are satisfied:
+ *                    - D = DP mod P-1 if P, D, DP != NULL
+ *                    - Q = DQ mod P-1 if P, D, DQ != NULL
+ *                    - QP = Q^-1 mod P if P, Q, QP != NULL
+ *                 - \c MBEDTLS_ERR_RSA_KEY_CHECK_FAILED if check failed,
+ *                   potentially including \c MBEDTLS_ERR_MPI_XXX if some
+ *                   MPI calculations failed.
+ *                 - \c MBEDTLS_ERR_RSA_BAD_INPUT_DATA if insufficient
+ *                   data was provided to check DP, DQ or QP.
+ *
+ * \note           The function can be used with a restricted set of arguments
+ *                 to perform specific checks only. E.g., calling it with the
+ *                 parameters (P, -, D, DP, -, -) will check DP = D mod P-1.
+ */
+int mbedtls_rsa_validate_crt( const mbedtls_mpi *P,  const mbedtls_mpi *Q,
+                              const mbedtls_mpi *D,  const mbedtls_mpi *DP,
+                              const mbedtls_mpi *DQ, const mbedtls_mpi *QP );
+
+#endif /* rsa_internal.h */

library/CMakeLists.txt

@@ -48,6 +48,7 @@ set(src_crypto
     platform.c
     ripemd160.c
     rsa.c
+    rsa_internal.c
     sha1.c
     sha256.c
     sha512.c

library/Makefile

@@ -59,9 +59,9 @@ OBJS_CRYPTO=	aes.o		aesni.o		arc4.o		\
 		padlock.o	pem.o		pk.o		\
 		pk_wrap.o	pkcs12.o	pkcs5.o		\
 		pkparse.o	pkwrite.o	platform.o	\
-		ripemd160.o	rsa.o		sha1.o		\
+		ripemd160.o	rsa_internal.o	rsa.o  		\
-		sha256.o	sha512.o	threading.o	\
+		sha1.o		sha256.o	sha512.o	\
-		timing.o	version.o			\
+		threading.o	timing.o	version.o	\
 		version_features.o		xtea.o
 
 OBJS_X509=	certs.o		pkcs11.o	x509.o		\

library/pk_wrap.c

@@ -68,7 +68,8 @@ static int rsa_can_do( mbedtls_pk_type_t type )
 
 static size_t rsa_get_bitlen( const void *ctx )
 {
-    return( 8 * ((const mbedtls_rsa_context *) ctx)->len );
+    const mbedtls_rsa_context * rsa = (const mbedtls_rsa_context *) ctx;
+    return( 8 * mbedtls_rsa_get_len( rsa ) );
 }
 
 static int rsa_verify_wrap( void *ctx, mbedtls_md_type_t md_alg,
@@ -76,21 +77,23 @@ static int rsa_verify_wrap( void *ctx, mbedtls_md_type_t md_alg,
                    const unsigned char *sig, size_t sig_len )
 {
     int ret;
+    mbedtls_rsa_context * rsa = (mbedtls_rsa_context *) ctx;
+    size_t rsa_len = mbedtls_rsa_get_len( rsa );
 
 #if SIZE_MAX > UINT_MAX
     if( md_alg == MBEDTLS_MD_NONE && UINT_MAX < hash_len )
         return( MBEDTLS_ERR_PK_BAD_INPUT_DATA );
 #endif /* SIZE_MAX > UINT_MAX */
 
-    if( sig_len < ((mbedtls_rsa_context *) ctx)->len )
+    if( sig_len < rsa_len )
         return( MBEDTLS_ERR_RSA_VERIFY_FAILED );
 
-    if( ( ret = mbedtls_rsa_pkcs1_verify( (mbedtls_rsa_context *) ctx, NULL, NULL,
+    if( ( ret = mbedtls_rsa_pkcs1_verify( rsa, NULL, NULL,
                                   MBEDTLS_RSA_PUBLIC, md_alg,
                                   (unsigned int) hash_len, hash, sig ) ) != 0 )
         return( ret );
 
-    if( sig_len > ((mbedtls_rsa_context *) ctx)->len )
+    if( sig_len > rsa_len )
         return( MBEDTLS_ERR_PK_SIG_LEN_MISMATCH );
 
     return( 0 );
@@ -101,14 +104,16 @@ static int rsa_sign_wrap( void *ctx, mbedtls_md_type_t md_alg,
                    unsigned char *sig, size_t *sig_len,
                    int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
 {
+    mbedtls_rsa_context * rsa = (mbedtls_rsa_context *) ctx;
+
 #if SIZE_MAX > UINT_MAX
     if( md_alg == MBEDTLS_MD_NONE && UINT_MAX < hash_len )
         return( MBEDTLS_ERR_PK_BAD_INPUT_DATA );
 #endif /* SIZE_MAX > UINT_MAX */
 
-    *sig_len = ((mbedtls_rsa_context *) ctx)->len;
+    *sig_len = mbedtls_rsa_get_len( rsa );
 
-    return( mbedtls_rsa_pkcs1_sign( (mbedtls_rsa_context *) ctx, f_rng, p_rng, MBEDTLS_RSA_PRIVATE,
+    return( mbedtls_rsa_pkcs1_sign( rsa, f_rng, p_rng, MBEDTLS_RSA_PRIVATE,
                 md_alg, (unsigned int) hash_len, hash, sig ) );
 }
 
@@ -117,10 +122,12 @@ static int rsa_decrypt_wrap( void *ctx,
                     unsigned char *output, size_t *olen, size_t osize,
                     int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
 {
-    if( ilen != ((mbedtls_rsa_context *) ctx)->len )
+    mbedtls_rsa_context * rsa = (mbedtls_rsa_context *) ctx;
+
+    if( ilen != mbedtls_rsa_get_len( rsa ) )
         return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
 
-    return( mbedtls_rsa_pkcs1_decrypt( (mbedtls_rsa_context *) ctx, f_rng, p_rng,
+    return( mbedtls_rsa_pkcs1_decrypt( rsa, f_rng, p_rng,
                 MBEDTLS_RSA_PRIVATE, olen, input, output, osize ) );
 }
 
@@ -129,13 +136,14 @@ static int rsa_encrypt_wrap( void *ctx,
                     unsigned char *output, size_t *olen, size_t osize,
                     int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
 {
-    *olen = ((mbedtls_rsa_context *) ctx)->len;
+    mbedtls_rsa_context * rsa = (mbedtls_rsa_context *) ctx;
+    *olen = mbedtls_rsa_get_len( rsa );
 
     if( *olen > osize )
         return( MBEDTLS_ERR_RSA_OUTPUT_TOO_LARGE );
 
-    return( mbedtls_rsa_pkcs1_encrypt( (mbedtls_rsa_context *) ctx,
+    return( mbedtls_rsa_pkcs1_encrypt( rsa, f_rng, p_rng, MBEDTLS_RSA_PUBLIC,
-                f_rng, p_rng, MBEDTLS_RSA_PUBLIC, ilen, input, output ) );
+                                       ilen, input, output ) );
 }
 
 static int rsa_check_pair_wrap( const void *pub, const void *prv )

library/pkparse.c

@@ -523,19 +523,36 @@ static int pk_get_rsapubkey( unsigned char **p,
         return( MBEDTLS_ERR_PK_INVALID_PUBKEY +
                 MBEDTLS_ERR_ASN1_LENGTH_MISMATCH );
 
-    if( ( ret = mbedtls_asn1_get_mpi( p, end, &rsa->N ) ) != 0 ||
+    /* Import N */
-        ( ret = mbedtls_asn1_get_mpi( p, end, &rsa->E ) ) != 0 )
+    if( ( ret = mbedtls_asn1_get_tag( p, end, &len, MBEDTLS_ASN1_INTEGER ) ) != 0 )
         return( MBEDTLS_ERR_PK_INVALID_PUBKEY + ret );
 
+    if( ( ret = mbedtls_rsa_import_raw( rsa, *p, len, NULL, 0, NULL, 0,
+                                        NULL, 0, NULL, 0 ) ) != 0 )
+        return( MBEDTLS_ERR_PK_INVALID_PUBKEY );
+
+    *p += len;
+
+    /* Import E */
+    if( ( ret = mbedtls_asn1_get_tag( p, end, &len, MBEDTLS_ASN1_INTEGER ) ) != 0 )
+        return( MBEDTLS_ERR_PK_INVALID_PUBKEY + ret );
+
+    if( ( ret = mbedtls_rsa_import_raw( rsa, NULL, 0, NULL, 0, NULL, 0,
+                                        NULL, 0, *p, len ) ) != 0 )
+        return( MBEDTLS_ERR_PK_INVALID_PUBKEY );
+
+    *p += len;
+
+    if( mbedtls_rsa_complete( rsa ) != 0 ||
+        mbedtls_rsa_check_pubkey( rsa ) != 0 )
+    {
+        return( MBEDTLS_ERR_PK_INVALID_PUBKEY );
+    }
+
     if( *p != end )
         return( MBEDTLS_ERR_PK_INVALID_PUBKEY +
                 MBEDTLS_ERR_ASN1_LENGTH_MISMATCH );
 
-    if( ( ret = mbedtls_rsa_check_pubkey( rsa ) ) != 0 )
-        return( MBEDTLS_ERR_PK_INVALID_PUBKEY );
-
-    rsa->len = mbedtls_mpi_size( &rsa->N );
-
     return( 0 );
 }
 #endif /* MBEDTLS_RSA_C */
@@ -646,10 +663,13 @@ static int pk_parse_key_pkcs1_der( mbedtls_rsa_context *rsa,
                                    const unsigned char *key,
                                    size_t keylen )
 {
-    int ret;
+    int ret, version;
     size_t len;
     unsigned char *p, *end;
 
+    mbedtls_mpi T;
+    mbedtls_mpi_init( &T );
+
     p = (unsigned char *) key;
     end = p + keylen;
 
@@ -677,45 +697,88 @@ static int pk_parse_key_pkcs1_der( mbedtls_rsa_context *rsa,
 
     end = p + len;
 
-    if( ( ret = mbedtls_asn1_get_int( &p, end, &rsa->ver ) ) != 0 )
+    if( ( ret = mbedtls_asn1_get_int( &p, end, &version ) ) != 0 )
     {
         return( MBEDTLS_ERR_PK_KEY_INVALID_FORMAT + ret );
     }
 
-    if( rsa->ver != 0 )
+    if( version != 0 )
     {
         return( MBEDTLS_ERR_PK_KEY_INVALID_VERSION );
     }
 
-    if( ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->N  ) ) != 0 ||
+    /* Import N */
-        ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->E  ) ) != 0 ||
+    if( ( ret = mbedtls_asn1_get_tag( &p, end, &len,
-        ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->D  ) ) != 0 ||
+                                      MBEDTLS_ASN1_INTEGER ) ) != 0 ||
-        ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->P  ) ) != 0 ||
+        ( ret = mbedtls_rsa_import_raw( rsa, p, len, NULL, 0, NULL, 0,
-        ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->Q  ) ) != 0 ||
+                                        NULL, 0, NULL, 0 ) ) != 0 )
-        ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->DP ) ) != 0 ||
+        goto cleanup;
-        ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->DQ ) ) != 0 ||
+    p += len;
-        ( ret = mbedtls_asn1_get_mpi( &p, end, &rsa->QP ) ) != 0 )
-    {
-        mbedtls_rsa_free( rsa );
-        return( MBEDTLS_ERR_PK_KEY_INVALID_FORMAT + ret );
-    }
 
-    rsa->len = mbedtls_mpi_size( &rsa->N );
+    /* Import E */
+    if( ( ret = mbedtls_asn1_get_tag( &p, end, &len,
+                                      MBEDTLS_ASN1_INTEGER ) ) != 0 ||
+        ( ret = mbedtls_rsa_import_raw( rsa, NULL, 0, NULL, 0, NULL, 0,
+                                        NULL, 0, p, len ) ) != 0 )
+        goto cleanup;
+    p += len;
+
+    /* Import D */
+    if( ( ret = mbedtls_asn1_get_tag( &p, end, &len,
+                                      MBEDTLS_ASN1_INTEGER ) ) != 0 ||
+        ( ret = mbedtls_rsa_import_raw( rsa, NULL, 0, NULL, 0, NULL, 0,
+                                        p, len, NULL, 0 ) ) != 0 )
+        goto cleanup;
+    p += len;
+
+    /* Import P */
+    if( ( ret = mbedtls_asn1_get_tag( &p, end, &len,
+                                      MBEDTLS_ASN1_INTEGER ) ) != 0 ||
+        ( ret = mbedtls_rsa_import_raw( rsa, NULL, 0, p, len, NULL, 0,
+                                        NULL, 0, NULL, 0 ) ) != 0 )
+        goto cleanup;
+    p += len;
+
+    /* Import Q */
+    if( ( ret = mbedtls_asn1_get_tag( &p, end, &len,
+                                      MBEDTLS_ASN1_INTEGER ) ) != 0 ||
+        ( ret = mbedtls_rsa_import_raw( rsa, NULL, 0, NULL, 0, p, len,
+                                        NULL, 0, NULL, 0 ) ) != 0 )
+        goto cleanup;
+    p += len;
+
+    /* Complete the RSA private key */
+    if( ( ret = mbedtls_rsa_complete( rsa ) ) != 0 )
+        goto cleanup;
+
+    /* Check optional parameters */
+    if( ( ret = mbedtls_asn1_get_mpi( &p, end, &T ) ) != 0 ||
+        ( ret = mbedtls_asn1_get_mpi( &p, end, &T ) ) != 0 ||
+        ( ret = mbedtls_asn1_get_mpi( &p, end, &T ) ) != 0 )
+        goto cleanup;
 
     if( p != end )
     {
-        mbedtls_rsa_free( rsa );
+        ret = MBEDTLS_ERR_PK_KEY_INVALID_FORMAT +
-        return( MBEDTLS_ERR_PK_KEY_INVALID_FORMAT +
+              MBEDTLS_ERR_ASN1_LENGTH_MISMATCH ;
-                MBEDTLS_ERR_ASN1_LENGTH_MISMATCH );
     }
 
-    if( ( ret = mbedtls_rsa_check_privkey( rsa ) ) != 0 )
+cleanup:
+
+    mbedtls_mpi_free( &T );
+
+    if( ret != 0 )
     {
+        /* Wrap error code if it's coming from a lower level */
+        if( ( ret & 0xff80 ) == 0 )
+            ret = MBEDTLS_ERR_PK_KEY_INVALID_FORMAT + ret;
+        else
+            ret = MBEDTLS_ERR_PK_KEY_INVALID_FORMAT;
+
         mbedtls_rsa_free( rsa );
-        return( ret );
     }
 
-    return( 0 );
+    return( ret );
 }
 #endif /* MBEDTLS_RSA_C */
 

library/pkwrite.c

@@ -62,13 +62,31 @@
  *  }
  */
 static int pk_write_rsa_pubkey( unsigned char **p, unsigned char *start,
-                                  mbedtls_rsa_context *rsa )
+                                mbedtls_rsa_context *rsa )
 {
     int ret;
     size_t len = 0;
+    mbedtls_mpi T;
 
-    MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( p, start, &rsa->E ) );
+    mbedtls_mpi_init( &T );
-    MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( p, start, &rsa->N ) );
+
+    /* Export E */
+    if ( ( ret = mbedtls_rsa_export( rsa, NULL, NULL, NULL, NULL, &T ) ) != 0 ||
+         ( ret = mbedtls_asn1_write_mpi( p, start, &T ) ) < 0 )
+        goto end_of_export;
+    len += ret;
+
+    /* Export N */
+    if ( ( ret = mbedtls_rsa_export( rsa, &T, NULL, NULL, NULL, NULL ) ) != 0 ||
+         ( ret = mbedtls_asn1_write_mpi( p, start, &T ) ) < 0 )
+        goto end_of_export;
+    len += ret;
+
+end_of_export:
+
+    mbedtls_mpi_free( &T );
+    if( ret < 0 )
+        return( ret );
 
     MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_len( p, start, len ) );
     MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_tag( p, start, MBEDTLS_ASN1_CONSTRUCTED |
@@ -83,7 +101,7 @@ static int pk_write_rsa_pubkey( unsigned char **p, unsigned char *start,
  * EC public key is an EC point
  */
 static int pk_write_ec_pubkey( unsigned char **p, unsigned char *start,
-                                 mbedtls_ecp_keypair *ec )
+                               mbedtls_ecp_keypair *ec )
 {
     int ret;
     size_t len = 0;
@@ -111,7 +129,7 @@ static int pk_write_ec_pubkey( unsigned char **p, unsigned char *start,
  * }
  */
 static int pk_write_ec_param( unsigned char **p, unsigned char *start,
-                                mbedtls_ecp_keypair *ec )
+                              mbedtls_ecp_keypair *ec )
 {
     int ret;
     size_t len = 0;
@@ -128,7 +146,7 @@ static int pk_write_ec_param( unsigned char **p, unsigned char *start,
 #endif /* MBEDTLS_ECP_C */
 
 int mbedtls_pk_write_pubkey( unsigned char **p, unsigned char *start,
-                     const mbedtls_pk_context *key )
+                             const mbedtls_pk_context *key )
 {
     int ret;
     size_t len = 0;
@@ -205,21 +223,79 @@ int mbedtls_pk_write_key_der( mbedtls_pk_context *key, unsigned char *buf, size_
 #if defined(MBEDTLS_RSA_C)
     if( mbedtls_pk_get_type( key ) == MBEDTLS_PK_RSA )
     {
+        mbedtls_mpi T; /* Temporary holding the exported parameters */
         mbedtls_rsa_context *rsa = mbedtls_pk_rsa( *key );
 
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &c, buf, &rsa->QP ) );
+        /*
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &c, buf, &rsa->DQ ) );
+         * Export the parameters one after another to avoid simultaneous copies.
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &c, buf, &rsa->DP ) );
+         */
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &c, buf, &rsa->Q ) );
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &c, buf, &rsa->P ) );
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &c, buf, &rsa->D ) );
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &c, buf, &rsa->E ) );
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_mpi( &c, buf, &rsa->N ) );
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_int( &c, buf, 0 ) );
 
+        mbedtls_mpi_init( &T );
+
+        /* Export QP */
+        if( ( ret = mbedtls_rsa_export_crt( rsa, NULL, NULL, &T ) ) != 0 ||
+            ( ret = mbedtls_asn1_write_mpi( &c, buf, &T ) ) < 0 )
+            goto end_of_export;
+        len += ret;
+
+        /* Export DQ */
+        if( ( ret = mbedtls_rsa_export_crt( rsa, NULL, &T, NULL ) ) != 0 ||
+            ( ret = mbedtls_asn1_write_mpi( &c, buf, &T ) ) < 0 )
+            goto end_of_export;
+        len += ret;
+
+        /* Export DP */
+        if( ( ret = mbedtls_rsa_export_crt( rsa, &T, NULL, NULL ) ) != 0 ||
+            ( ret = mbedtls_asn1_write_mpi( &c, buf, &T ) ) < 0 )
+            goto end_of_export;
+        len += ret;
+
+        /* Export Q */
+        if ( ( ret = mbedtls_rsa_export( rsa, NULL, NULL,
+                                         &T, NULL, NULL ) ) != 0 ||
+             ( ret = mbedtls_asn1_write_mpi( &c, buf, &T ) ) < 0 )
+            goto end_of_export;
+        len += ret;
+
+        /* Export P */
+        if ( ( ret = mbedtls_rsa_export( rsa, NULL, &T,
+                                         NULL, NULL, NULL ) ) != 0 ||
+             ( ret = mbedtls_asn1_write_mpi( &c, buf, &T ) ) < 0 )
+            goto end_of_export;
+        len += ret;
+
+        /* Export D */
+        if ( ( ret = mbedtls_rsa_export( rsa, NULL, NULL,
+                                         NULL, &T, NULL ) ) != 0 ||
+             ( ret = mbedtls_asn1_write_mpi( &c, buf, &T ) ) < 0 )
+            goto end_of_export;
+        len += ret;
+
+        /* Export E */
+        if ( ( ret = mbedtls_rsa_export( rsa, NULL, NULL,
+                                         NULL, NULL, &T ) ) != 0 ||
+             ( ret = mbedtls_asn1_write_mpi( &c, buf, &T ) ) < 0 )
+            goto end_of_export;
+        len += ret;
+
+        /* Export N */
+        if ( ( ret = mbedtls_rsa_export( rsa, &T, NULL,
+                                         NULL, NULL, NULL ) ) != 0 ||
+             ( ret = mbedtls_asn1_write_mpi( &c, buf, &T ) ) < 0 )
+            goto end_of_export;
+        len += ret;
+
+    end_of_export:
+
+        mbedtls_mpi_free( &T );
+        if( ret < 0 )
+            return( ret );
+
+        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_int( &c, buf, 0 ) );
         MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_len( &c, buf, len ) );
-        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_tag( &c, buf, MBEDTLS_ASN1_CONSTRUCTED |
+        MBEDTLS_ASN1_CHK_ADD( len, mbedtls_asn1_write_tag( &c,
-                                                    MBEDTLS_ASN1_SEQUENCE ) );
+                                               buf, MBEDTLS_ASN1_CONSTRUCTED |
+                                               MBEDTLS_ASN1_SEQUENCE ) );
     }
     else
 #endif /* MBEDTLS_RSA_C */

library/rsa.c

@@ -18,6 +18,7 @@
  *
  *  This file is part of mbed TLS (https://tls.mbed.org)
  */
+
 /*
  *  The following sources were referenced in the design of this implementation
  *  of the RSA algorithm:
@@ -45,6 +46,7 @@
 #if defined(MBEDTLS_RSA_C)
 
 #include "mbedtls/rsa.h"
+#include "mbedtls/rsa_internal.h"
 #include "mbedtls/oid.h"
 
 #include <string.h>
@@ -66,11 +68,378 @@
 #define mbedtls_free   free
 #endif
 
+#if !defined(MBEDTLS_RSA_ALT)
+
 /* Implementation that should never be optimized out by the compiler */
 static void mbedtls_zeroize( void *v, size_t n ) {
     volatile unsigned char *p = (unsigned char*)v; while( n-- ) *p++ = 0;
 }
 
+int mbedtls_rsa_import( mbedtls_rsa_context *ctx,
+                        const mbedtls_mpi *N,
+                        const mbedtls_mpi *P, const mbedtls_mpi *Q,
+                        const mbedtls_mpi *D, const mbedtls_mpi *E )
+{
+    int ret;
+
+    if( ( N != NULL && ( ret = mbedtls_mpi_copy( &ctx->N, N ) ) != 0 ) ||
+        ( P != NULL && ( ret = mbedtls_mpi_copy( &ctx->P, P ) ) != 0 ) ||
+        ( Q != NULL && ( ret = mbedtls_mpi_copy( &ctx->Q, Q ) ) != 0 ) ||
+        ( D != NULL && ( ret = mbedtls_mpi_copy( &ctx->D, D ) ) != 0 ) ||
+        ( E != NULL && ( ret = mbedtls_mpi_copy( &ctx->E, E ) ) != 0 ) )
+    {
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
+    }
+
+    if( N != NULL )
+        ctx->len = mbedtls_mpi_size( &ctx->N );
+
+    return( 0 );
+}
+
+int mbedtls_rsa_import_raw( mbedtls_rsa_context *ctx,
+                            unsigned char const *N, size_t N_len,
+                            unsigned char const *P, size_t P_len,
+                            unsigned char const *Q, size_t Q_len,
+                            unsigned char const *D, size_t D_len,
+                            unsigned char const *E, size_t E_len )
+{
+    int ret;
+
+    if( N != NULL )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->N, N, N_len ) );
+        ctx->len = mbedtls_mpi_size( &ctx->N );
+    }
+
+    if( P != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->P, P, P_len ) );
+
+    if( Q != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->Q, Q, Q_len ) );
+
+    if( D != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->D, D, D_len ) );
+
+    if( E != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &ctx->E, E, E_len ) );
+
+cleanup:
+
+    if( ret != 0 )
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
+
+    return( 0 );
+}
+
+/*
+ * Checks whether the context fields are set in such a way
+ * that the RSA primitives will be able to execute without error.
+ * It does *not* make guarantees for consistency of the parameters.
+ */
+static int rsa_check_context( mbedtls_rsa_context const *ctx, int is_priv,
+                              int blinding_needed )
+{
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    /* blinding_needed is only used for NO_CRT to decide whether
+     * P,Q need to be present or not. */
+    ((void) blinding_needed);
+#endif
+
+    if( ctx->len != mbedtls_mpi_size( &ctx->N ) ||
+        ctx->len > MBEDTLS_MPI_MAX_SIZE )
+    {
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+    }
+
+    /*
+     * 1. Modular exponentiation needs positive, odd moduli.
+     */
+
+    /* Modular exponentiation wrt. N is always used for
+     * RSA public key operations. */
+    if( mbedtls_mpi_cmp_int( &ctx->N, 0 ) <= 0 ||
+        mbedtls_mpi_get_bit( &ctx->N, 0 ) == 0  )
+    {
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+    }
+
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    /* Modular exponentiation for P and Q is only
+     * used for private key operations and if CRT
+     * is used. */
+    if( is_priv &&
+        ( mbedtls_mpi_cmp_int( &ctx->P, 0 ) <= 0 ||
+          mbedtls_mpi_get_bit( &ctx->P, 0 ) == 0 ||
+          mbedtls_mpi_cmp_int( &ctx->Q, 0 ) <= 0 ||
+          mbedtls_mpi_get_bit( &ctx->Q, 0 ) == 0  ) )
+    {
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+    }
+#endif /* !MBEDTLS_RSA_NO_CRT */
+
+    /*
+     * 2. Exponents must be positive
+     */
+
+    /* Always need E for public key operations */
+    if( mbedtls_mpi_cmp_int( &ctx->E, 0 ) <= 0 )
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+
+#if defined(MBEDTLS_RSA_NO_CRT)
+    /* For private key operations, use D or DP & DQ
+     * as (unblinded) exponents. */
+    if( is_priv && mbedtls_mpi_cmp_int( &ctx->D, 0 ) <= 0 )
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+#else
+    if( is_priv &&
+        ( mbedtls_mpi_cmp_int( &ctx->DP, 0 ) <= 0 ||
+          mbedtls_mpi_cmp_int( &ctx->DQ, 0 ) <= 0  ) )
+    {
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+    }
+#endif /* MBEDTLS_RSA_NO_CRT */
+
+    /* Blinding shouldn't make exponents negative either,
+     * so check that P, Q >= 1 if that hasn't yet been
+     * done as part of 1. */
+#if defined(MBEDTLS_RSA_NO_CRT)
+    if( is_priv && blinding_needed &&
+        ( mbedtls_mpi_cmp_int( &ctx->P, 0 ) <= 0 ||
+          mbedtls_mpi_cmp_int( &ctx->Q, 0 ) <= 0 ) )
+    {
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+    }
+#endif
+
+    /* It wouldn't lead to an error if it wasn't satisfied,
+     * but check for QP >= 1 nonetheless. */
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    if( is_priv &&
+        mbedtls_mpi_cmp_int( &ctx->QP, 0 ) <= 0 )
+    {
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+    }
+#endif
+
+    return( 0 );
+}
+
+int mbedtls_rsa_complete( mbedtls_rsa_context *ctx )
+{
+    int ret = 0;
+
+    const int have_N = ( mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 );
+    const int have_P = ( mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 );
+    const int have_Q = ( mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 );
+    const int have_D = ( mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 );
+    const int have_E = ( mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0 );
+
+    /*
+     * Check whether provided parameters are enough
+     * to deduce all others. The following incomplete
+     * parameter sets for private keys are supported:
+     *
+     * (1) P, Q missing.
+     * (2) D and potentially N missing.
+     *
+     */
+
+    const int n_missing  =              have_P &&  have_Q &&  have_D && have_E;
+    const int pq_missing =   have_N && !have_P && !have_Q &&  have_D && have_E;
+    const int d_missing  =              have_P &&  have_Q && !have_D && have_E;
+    const int is_pub     =   have_N && !have_P && !have_Q && !have_D && have_E;
+
+    /* These three alternatives are mutually exclusive */
+    const int is_priv = n_missing || pq_missing || d_missing;
+
+    if( !is_priv && !is_pub )
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+
+    /*
+     * Step 1: Deduce N if P, Q are provided.
+     */
+
+    if( !have_N && have_P && have_Q )
+    {
+        if( ( ret = mbedtls_mpi_mul_mpi( &ctx->N, &ctx->P,
+                                         &ctx->Q ) ) != 0 )
+        {
+            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
+        }
+
+        ctx->len = mbedtls_mpi_size( &ctx->N );
+    }
+
+    /*
+     * Step 2: Deduce and verify all remaining core parameters.
+     */
+
+    if( pq_missing )
+    {
+        ret = mbedtls_rsa_deduce_primes( &ctx->N, &ctx->E, &ctx->D,
+                                         &ctx->P, &ctx->Q );
+        if( ret != 0 )
+            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
+
+    }
+    else if( d_missing )
+    {
+        if( ( ret = mbedtls_rsa_deduce_private_exponent( &ctx->P,
+                                                         &ctx->Q,
+                                                         &ctx->E,
+                                                         &ctx->D ) ) != 0 )
+        {
+            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
+        }
+    }
+
+    /*
+     * Step 3: Deduce all additional parameters specific
+     *         to our current RSA implementation.
+     */
+
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    if( is_priv )
+    {
+        ret = mbedtls_rsa_deduce_crt( &ctx->P,  &ctx->Q,  &ctx->D,
+                                      &ctx->DP, &ctx->DQ, &ctx->QP );
+        if( ret != 0 )
+            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
+    }
+#endif /* MBEDTLS_RSA_NO_CRT */
+
+    /*
+     * Step 3: Basic sanity checks
+     */
+
+    return( rsa_check_context( ctx, is_priv, 1 ) );
+}
+
+int mbedtls_rsa_export_raw( const mbedtls_rsa_context *ctx,
+                            unsigned char *N, size_t N_len,
+                            unsigned char *P, size_t P_len,
+                            unsigned char *Q, size_t Q_len,
+                            unsigned char *D, size_t D_len,
+                            unsigned char *E, size_t E_len )
+{
+    int ret = 0;
+
+    /* Check if key is private or public */
+    const int is_priv =
+        mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0;
+
+    if( !is_priv )
+    {
+        /* If we're trying to export private parameters for a public key,
+         * something must be wrong. */
+        if( P != NULL || Q != NULL || D != NULL )
+            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+
+    }
+
+    if( N != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->N, N, N_len ) );
+
+    if( P != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->P, P, P_len ) );
+
+    if( Q != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->Q, Q, Q_len ) );
+
+    if( D != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->D, D, D_len ) );
+
+    if( E != NULL )
+        MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->E, E, E_len ) );
+
+cleanup:
+
+    return( ret );
+}
+
+int mbedtls_rsa_export( const mbedtls_rsa_context *ctx,
+                        mbedtls_mpi *N, mbedtls_mpi *P, mbedtls_mpi *Q,
+                        mbedtls_mpi *D, mbedtls_mpi *E )
+{
+    int ret;
+
+    /* Check if key is private or public */
+    int is_priv =
+        mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0;
+
+    if( !is_priv )
+    {
+        /* If we're trying to export private parameters for a public key,
+         * something must be wrong. */
+        if( P != NULL || Q != NULL || D != NULL )
+            return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+
+    }
+
+    /* Export all requested core parameters. */
+
+    if( ( N != NULL && ( ret = mbedtls_mpi_copy( N, &ctx->N ) ) != 0 ) ||
+        ( P != NULL && ( ret = mbedtls_mpi_copy( P, &ctx->P ) ) != 0 ) ||
+        ( Q != NULL && ( ret = mbedtls_mpi_copy( Q, &ctx->Q ) ) != 0 ) ||
+        ( D != NULL && ( ret = mbedtls_mpi_copy( D, &ctx->D ) ) != 0 ) ||
+        ( E != NULL && ( ret = mbedtls_mpi_copy( E, &ctx->E ) ) != 0 ) )
+    {
+        return( ret );
+    }
+
+    return( 0 );
+}
+
+/*
+ * Export CRT parameters
+ * This must also be implemented if CRT is not used, for being able to
+ * write DER encoded RSA keys. The helper function mbedtls_rsa_deduce_crt
+ * can be used in this case.
+ */
+int mbedtls_rsa_export_crt( const mbedtls_rsa_context *ctx,
+                            mbedtls_mpi *DP, mbedtls_mpi *DQ, mbedtls_mpi *QP )
+{
+    int ret;
+
+    /* Check if key is private or public */
+    int is_priv =
+        mbedtls_mpi_cmp_int( &ctx->N, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->P, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->Q, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->D, 0 ) != 0 &&
+        mbedtls_mpi_cmp_int( &ctx->E, 0 ) != 0;
+
+    if( !is_priv )
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    /* Export all requested blinding parameters. */
+    if( ( DP != NULL && ( ret = mbedtls_mpi_copy( DP, &ctx->DP ) ) != 0 ) ||
+        ( DQ != NULL && ( ret = mbedtls_mpi_copy( DQ, &ctx->DQ ) ) != 0 ) ||
+        ( QP != NULL && ( ret = mbedtls_mpi_copy( QP, &ctx->QP ) ) != 0 ) )
+    {
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
+    }
+#else
+    if( ( ret = mbedtls_rsa_deduce_crt( &ctx->P, &ctx->Q, &ctx->D,
+                                        DP, DQ, QP ) ) != 0 )
+    {
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA + ret );
+    }
+#endif
+
+    return( 0 );
+}
+
 /*
  * Initialize an RSA context
  */
@@ -96,6 +465,16 @@ void mbedtls_rsa_set_padding( mbedtls_rsa_context *ctx, int padding, int hash_id
     ctx->hash_id = hash_id;
 }
 
+/*
+ * Get length in bytes of RSA modulus
+ */
+
+size_t mbedtls_rsa_get_len( const mbedtls_rsa_context *ctx )
+{
+    return( ctx->len );
+}
+
+
 #if defined(MBEDTLS_GENPRIME)
 
 /*
@@ -107,7 +486,7 @@ int mbedtls_rsa_gen_key( mbedtls_rsa_context *ctx,
                  unsigned int nbits, int exponent )
 {
     int ret;
-    mbedtls_mpi P1, Q1, H, G;
+    mbedtls_mpi H, G;
 
     if( f_rng == NULL || nbits < 128 || exponent < 3 )
         return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
@@ -115,8 +494,8 @@ int mbedtls_rsa_gen_key( mbedtls_rsa_context *ctx,
     if( nbits % 2 )
         return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
 
-    mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 );
+    mbedtls_mpi_init( &H );
-    mbedtls_mpi_init( &H ); mbedtls_mpi_init( &G );
+    mbedtls_mpi_init( &G );
 
     /*
      * find primes P and Q with Q < P so that:
@@ -127,10 +506,10 @@ int mbedtls_rsa_gen_key( mbedtls_rsa_context *ctx,
     do
     {
         MBEDTLS_MPI_CHK( mbedtls_mpi_gen_prime( &ctx->P, nbits >> 1, 0,
-                                f_rng, p_rng ) );
+                                                f_rng, p_rng ) );
 
         MBEDTLS_MPI_CHK( mbedtls_mpi_gen_prime( &ctx->Q, nbits >> 1, 0,
-                                f_rng, p_rng ) );
+                                                f_rng, p_rng ) );
 
         if( mbedtls_mpi_cmp_mpi( &ctx->P, &ctx->Q ) == 0 )
             continue;
@@ -140,31 +519,43 @@ int mbedtls_rsa_gen_key( mbedtls_rsa_context *ctx,
             continue;
 
         if( mbedtls_mpi_cmp_mpi( &ctx->P, &ctx->Q ) < 0 )
-                                mbedtls_mpi_swap( &ctx->P, &ctx->Q );
+            mbedtls_mpi_swap( &ctx->P, &ctx->Q );
 
-        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &P1, &ctx->P, 1 ) );
+        /* Temporarily replace P,Q by P-1, Q-1 */
-        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &Q1, &ctx->Q, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &ctx->P, &ctx->P, 1 ) );
-        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &H, &P1, &Q1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &ctx->Q, &ctx->Q, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &H, &ctx->P, &ctx->Q ) );
         MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, &ctx->E, &H  ) );
     }
     while( mbedtls_mpi_cmp_int( &G, 1 ) != 0 );
 
+    /* Restore P,Q */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &ctx->P,  &ctx->P, 1 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &ctx->Q,  &ctx->Q, 1 ) );
+
+    ctx->len = mbedtls_mpi_size( &ctx->N );
+
     /*
      * D  = E^-1 mod ((P-1)*(Q-1))
      * DP = D mod (P - 1)
      * DQ = D mod (Q - 1)
      * QP = Q^-1 mod P
      */
-    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->D , &ctx->E, &H  ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->DP, &ctx->D, &P1 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->DQ, &ctx->D, &Q1 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->QP, &ctx->Q, &ctx->P ) );
 
-    ctx->len = ( mbedtls_mpi_bitlen( &ctx->N ) + 7 ) >> 3;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &ctx->D, &ctx->E, &H  ) );
+
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    MBEDTLS_MPI_CHK( mbedtls_rsa_deduce_crt( &ctx->P, &ctx->Q, &ctx->D,
+                                             &ctx->DP, &ctx->DQ, &ctx->QP ) );
+#endif /* MBEDTLS_RSA_NO_CRT */
+
+    /* Double-check */
+    MBEDTLS_MPI_CHK( mbedtls_rsa_check_privkey( ctx ) );
 
 cleanup:
 
-    mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &H ); mbedtls_mpi_free( &G );
+    mbedtls_mpi_free( &H );
+    mbedtls_mpi_free( &G );
 
     if( ret != 0 )
     {
@@ -182,82 +573,48 @@ cleanup:
  */
 int mbedtls_rsa_check_pubkey( const mbedtls_rsa_context *ctx )
 {
-    if( !ctx->N.p || !ctx->E.p )
+    if( rsa_check_context( ctx, 0 /* public */, 0 /* no blinding */ ) != 0 )
         return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
 
-    if( ( ctx->N.p[0] & 1 ) == 0 ||
+    if( mbedtls_mpi_bitlen( &ctx->N ) < 128 )
-        ( ctx->E.p[0] & 1 ) == 0 )
+    {
         return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
+    }
 
-    if( mbedtls_mpi_bitlen( &ctx->N ) < 128 ||
+    if( mbedtls_mpi_get_bit( &ctx->E, 0 ) == 0 ||
-        mbedtls_mpi_bitlen( &ctx->N ) > MBEDTLS_MPI_MAX_BITS )
+        mbedtls_mpi_bitlen( &ctx->E )     < 2  ||
-        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
-
-    if( mbedtls_mpi_bitlen( &ctx->E ) < 2 ||
         mbedtls_mpi_cmp_mpi( &ctx->E, &ctx->N ) >= 0 )
+    {
         return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
+    }
 
     return( 0 );
 }
 
 /*
- * Check a private RSA key
+ * Check for the consistency of all fields in an RSA private key context
  */
 int mbedtls_rsa_check_privkey( const mbedtls_rsa_context *ctx )
 {
-    int ret;
+    if( mbedtls_rsa_check_pubkey( ctx ) != 0 ||
-    mbedtls_mpi PQ, DE, P1, Q1, H, I, G, G2, L1, L2, DP, DQ, QP;
+        rsa_check_context( ctx, 1 /* private */, 1 /* blinding */ ) != 0 )
-
-    if( ( ret = mbedtls_rsa_check_pubkey( ctx ) ) != 0 )
-        return( ret );
-
-    if( !ctx->P.p || !ctx->Q.p || !ctx->D.p )
-        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
-
-    mbedtls_mpi_init( &PQ ); mbedtls_mpi_init( &DE ); mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 );
-    mbedtls_mpi_init( &H  ); mbedtls_mpi_init( &I  ); mbedtls_mpi_init( &G  ); mbedtls_mpi_init( &G2 );
-    mbedtls_mpi_init( &L1 ); mbedtls_mpi_init( &L2 ); mbedtls_mpi_init( &DP ); mbedtls_mpi_init( &DQ );
-    mbedtls_mpi_init( &QP );
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &PQ, &ctx->P, &ctx->Q ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &DE, &ctx->D, &ctx->E ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &P1, &ctx->P, 1 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &Q1, &ctx->Q, 1 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &H, &P1, &Q1 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G, &ctx->E, &H  ) );
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( &G2, &P1, &Q1 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &L1, &L2, &H, &G2 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &I, &DE, &L1  ) );
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &DP, &ctx->D, &P1 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &DQ, &ctx->D, &Q1 ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( &QP, &ctx->Q, &ctx->P ) );
-    /*
-     * Check for a valid PKCS1v2 private key
-     */
-    if( mbedtls_mpi_cmp_mpi( &PQ, &ctx->N ) != 0 ||
-        mbedtls_mpi_cmp_mpi( &DP, &ctx->DP ) != 0 ||
-        mbedtls_mpi_cmp_mpi( &DQ, &ctx->DQ ) != 0 ||
-        mbedtls_mpi_cmp_mpi( &QP, &ctx->QP ) != 0 ||
-        mbedtls_mpi_cmp_int( &L2, 0 ) != 0 ||
-        mbedtls_mpi_cmp_int( &I, 1 ) != 0 ||
-        mbedtls_mpi_cmp_int( &G, 1 ) != 0 )
     {
-        ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
     }
 
-cleanup:
+    if( mbedtls_rsa_validate_params( &ctx->N, &ctx->P, &ctx->Q,
-    mbedtls_mpi_free( &PQ ); mbedtls_mpi_free( &DE ); mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 );
+                                     &ctx->D, &ctx->E, NULL, NULL ) != 0 )
-    mbedtls_mpi_free( &H  ); mbedtls_mpi_free( &I  ); mbedtls_mpi_free( &G  ); mbedtls_mpi_free( &G2 );
+    {
-    mbedtls_mpi_free( &L1 ); mbedtls_mpi_free( &L2 ); mbedtls_mpi_free( &DP ); mbedtls_mpi_free( &DQ );
+        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
-    mbedtls_mpi_free( &QP );
+    }
 
-    if( ret == MBEDTLS_ERR_RSA_KEY_CHECK_FAILED )
+#if !defined(MBEDTLS_RSA_NO_CRT)
-        return( ret );
+    else if( mbedtls_rsa_validate_crt( &ctx->P, &ctx->Q, &ctx->D,
-
+                                       &ctx->DP, &ctx->DQ, &ctx->QP ) != 0 )
-    if( ret != 0 )
+    {
-        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED + ret );
+        return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
+    }
+#endif
 
     return( 0 );
 }
@@ -265,9 +622,10 @@ cleanup:
 /*
  * Check if contexts holding a public and private key match
  */
-int mbedtls_rsa_check_pub_priv( const mbedtls_rsa_context *pub, const mbedtls_rsa_context *prv )
+int mbedtls_rsa_check_pub_priv( const mbedtls_rsa_context *pub,
+                                const mbedtls_rsa_context *prv )
 {
-    if( mbedtls_rsa_check_pubkey( pub ) != 0 ||
+    if( mbedtls_rsa_check_pubkey( pub )  != 0 ||
         mbedtls_rsa_check_privkey( prv ) != 0 )
     {
         return( MBEDTLS_ERR_RSA_KEY_CHECK_FAILED );
@@ -293,6 +651,9 @@ int mbedtls_rsa_public( mbedtls_rsa_context *ctx,
     size_t olen;
     mbedtls_mpi T;
 
+    if( rsa_check_context( ctx, 0 /* public */, 0 /* no blinding */ ) )
+        return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+
     mbedtls_mpi_init( &T );
 
 #if defined(MBEDTLS_THREADING_C)
@@ -409,14 +770,15 @@ int mbedtls_rsa_private( mbedtls_rsa_context *ctx,
     mbedtls_mpi *DQ = &ctx->DQ;
 #endif
 
-    /* Make sure we have private key info, prevent possible misuse */
+    if( rsa_check_context( ctx, 1             /* private key checks */,
-    if( ctx->P.p == NULL || ctx->Q.p == NULL || ctx->D.p == NULL )
+                                f_rng != NULL /* blinding y/n       */ ) != 0 )
+    {
         return( MBEDTLS_ERR_RSA_BAD_INPUT_DATA );
+    }
 
     mbedtls_mpi_init( &T ); mbedtls_mpi_init( &T1 ); mbedtls_mpi_init( &T2 );
     mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 ); mbedtls_mpi_init( &R );
 
-
     if( f_rng != NULL )
     {
 #if defined(MBEDTLS_RSA_NO_CRT)
@@ -1630,13 +1992,16 @@ int mbedtls_rsa_copy( mbedtls_rsa_context *dst, const mbedtls_rsa_context *src )
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->D, &src->D ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->P, &src->P ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->Q, &src->Q ) );
+
+#if !defined(MBEDTLS_RSA_NO_CRT)
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->DP, &src->DP ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->DQ, &src->DQ ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->QP, &src->QP ) );
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RN, &src->RN ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RP, &src->RP ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RQ, &src->RQ ) );
+#endif
+
+    MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->RN, &src->RN ) );
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->Vi, &src->Vi ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_copy( &dst->Vf, &src->Vf ) );
@@ -1657,16 +2022,23 @@ cleanup:
 void mbedtls_rsa_free( mbedtls_rsa_context *ctx )
 {
     mbedtls_mpi_free( &ctx->Vi ); mbedtls_mpi_free( &ctx->Vf );
-    mbedtls_mpi_free( &ctx->RQ ); mbedtls_mpi_free( &ctx->RP ); mbedtls_mpi_free( &ctx->RN );
+    mbedtls_mpi_free( &ctx->RN ); mbedtls_mpi_free( &ctx->D  );
-    mbedtls_mpi_free( &ctx->QP ); mbedtls_mpi_free( &ctx->DQ ); mbedtls_mpi_free( &ctx->DP );
+    mbedtls_mpi_free( &ctx->Q  ); mbedtls_mpi_free( &ctx->P  );
-    mbedtls_mpi_free( &ctx->Q  ); mbedtls_mpi_free( &ctx->P  ); mbedtls_mpi_free( &ctx->D );
     mbedtls_mpi_free( &ctx->E  ); mbedtls_mpi_free( &ctx->N  );
 
+#if !defined(MBEDTLS_RSA_NO_CRT)
+    mbedtls_mpi_free( &ctx->RQ ); mbedtls_mpi_free( &ctx->RP );
+    mbedtls_mpi_free( &ctx->QP ); mbedtls_mpi_free( &ctx->DQ );
+    mbedtls_mpi_free( &ctx->DP );
+#endif /* MBEDTLS_RSA_NO_CRT */
+
 #if defined(MBEDTLS_THREADING_C)
     mbedtls_mutex_free( &ctx->mutex );
 #endif
 }
 
+#endif /* !MBEDTLS_RSA_ALT */
+
 #if defined(MBEDTLS_SELF_TEST)
 
 #include "mbedtls/sha1.h"
@@ -1706,21 +2078,6 @@ void mbedtls_rsa_free( mbedtls_rsa_context *ctx )
                 "910E4168387E3C30AA1E00C339A79508" \
                 "8452DD96A9A5EA5D9DCA68DA636032AF"
 
-#define RSA_DP  "C1ACF567564274FB07A0BBAD5D26E298" \
-                "3C94D22288ACD763FD8E5600ED4A702D" \
-                "F84198A5F06C2E72236AE490C93F07F8" \
-                "3CC559CD27BC2D1CA488811730BB5725"
-
-#define RSA_DQ  "4959CBF6F8FEF750AEE6977C155579C7" \
-                "D8AAEA56749EA28623272E4F7D0592AF" \
-                "7C1F1313CAC9471B5C523BFE592F517B" \
-                "407A1BD76C164B93DA2D32A383E58357"
-
-#define RSA_QP  "9AE7FBC99546432DF71896FC239EADAE" \
-                "F38D18D2B2F0E2DD275AA977E2BF4411" \
-                "F5A3B2A5D33605AEBBCCBA7FEB9F2D2F" \
-                "A74206CEC169D74BF5A8C50D6F48EA08"
-
 #define PT_LEN  24
 #define RSA_PT  "\xAA\xBB\xCC\x03\x02\x01\x00\xFF\xFF\xFF\xFF\xFF" \
                 "\x11\x22\x33\x0A\x0B\x0C\xCC\xDD\xDD\xDD\xDD\xDD"
@@ -1763,17 +2120,23 @@ int mbedtls_rsa_self_test( int verbose )
     unsigned char sha1sum[20];
 #endif
 
+    mbedtls_mpi K;
+
+    mbedtls_mpi_init( &K );
     mbedtls_rsa_init( &rsa, MBEDTLS_RSA_PKCS_V15, 0 );
 
-    rsa.len = KEY_LEN;
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_N  ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &rsa.N , 16, RSA_N  ) );
+    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, &K, NULL, NULL, NULL, NULL ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &rsa.E , 16, RSA_E  ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_P  ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &rsa.D , 16, RSA_D  ) );
+    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, &K, NULL, NULL, NULL ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &rsa.P , 16, RSA_P  ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_Q  ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &rsa.Q , 16, RSA_Q  ) );
+    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, NULL, &K, NULL, NULL ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &rsa.DP, 16, RSA_DP ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_D  ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &rsa.DQ, 16, RSA_DQ ) );
+    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, NULL, NULL, &K, NULL ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &rsa.QP, 16, RSA_QP ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_read_string( &K, 16, RSA_E  ) );
+    MBEDTLS_MPI_CHK( mbedtls_rsa_import( &rsa, NULL, NULL, NULL, NULL, &K ) );
+
+    MBEDTLS_MPI_CHK( mbedtls_rsa_complete( &rsa ) );
 
     if( verbose != 0 )
         mbedtls_printf( "  RSA key validation: " );
@@ -1792,8 +2155,9 @@ int mbedtls_rsa_self_test( int verbose )
 
     memcpy( rsa_plaintext, RSA_PT, PT_LEN );
 
-    if( mbedtls_rsa_pkcs1_encrypt( &rsa, myrand, NULL, MBEDTLS_RSA_PUBLIC, PT_LEN,
+    if( mbedtls_rsa_pkcs1_encrypt( &rsa, myrand, NULL, MBEDTLS_RSA_PUBLIC,
-                           rsa_plaintext, rsa_ciphertext ) != 0 )
+                                   PT_LEN, rsa_plaintext,
+                                   rsa_ciphertext ) != 0 )
     {
         if( verbose != 0 )
             mbedtls_printf( "failed\n" );
@@ -1804,9 +2168,9 @@ int mbedtls_rsa_self_test( int verbose )
     if( verbose != 0 )
         mbedtls_printf( "passed\n  PKCS#1 decryption : " );
 
-    if( mbedtls_rsa_pkcs1_decrypt( &rsa, myrand, NULL, MBEDTLS_RSA_PRIVATE, &len,
+    if( mbedtls_rsa_pkcs1_decrypt( &rsa, myrand, NULL, MBEDTLS_RSA_PRIVATE,
-                           rsa_ciphertext, rsa_decrypted,
+                                   &len, rsa_ciphertext, rsa_decrypted,
-                           sizeof(rsa_decrypted) ) != 0 )
+                                   sizeof(rsa_decrypted) ) != 0 )
     {
         if( verbose != 0 )
             mbedtls_printf( "failed\n" );
@@ -1831,8 +2195,9 @@ int mbedtls_rsa_self_test( int verbose )
 
     mbedtls_sha1( rsa_plaintext, PT_LEN, sha1sum );
 
-    if( mbedtls_rsa_pkcs1_sign( &rsa, myrand, NULL, MBEDTLS_RSA_PRIVATE, MBEDTLS_MD_SHA1, 0,
+    if( mbedtls_rsa_pkcs1_sign( &rsa, myrand, NULL,
-                        sha1sum, rsa_ciphertext ) != 0 )
+                                MBEDTLS_RSA_PRIVATE, MBEDTLS_MD_SHA1, 0,
+                                sha1sum, rsa_ciphertext ) != 0 )
     {
         if( verbose != 0 )
             mbedtls_printf( "failed\n" );
@@ -1843,8 +2208,9 @@ int mbedtls_rsa_self_test( int verbose )
     if( verbose != 0 )
         mbedtls_printf( "passed\n  PKCS#1 sig. verify: " );
 
-    if( mbedtls_rsa_pkcs1_verify( &rsa, NULL, NULL, MBEDTLS_RSA_PUBLIC, MBEDTLS_MD_SHA1, 0,
+    if( mbedtls_rsa_pkcs1_verify( &rsa, NULL, NULL,
-                          sha1sum, rsa_ciphertext ) != 0 )
+                                  MBEDTLS_RSA_PUBLIC, MBEDTLS_MD_SHA1, 0,
+                                  sha1sum, rsa_ciphertext ) != 0 )
     {
         if( verbose != 0 )
             mbedtls_printf( "failed\n" );
@@ -1860,6 +2226,7 @@ int mbedtls_rsa_self_test( int verbose )
         mbedtls_printf( "\n" );
 
 cleanup:
+    mbedtls_mpi_free( &K );
     mbedtls_rsa_free( &rsa );
 #else /* MBEDTLS_PKCS1_V15 */
     ((void) verbose);

library/rsa_internal.c

@@ -0,0 +1,487 @@
+/*
+ *  Helper functions for the RSA module
+ *
+ *  Copyright (C) 2006-2017, ARM Limited, All Rights Reserved
+ *  SPDX-License-Identifier: Apache-2.0
+ *
+ *  Licensed under the Apache License, Version 2.0 (the "License"); you may
+ *  not use this file except in compliance with the License.
+ *  You may obtain a copy of the License at
+ *
+ *  http://www.apache.org/licenses/LICENSE-2.0
+ *
+ *  Unless required by applicable law or agreed to in writing, software
+ *  distributed under the License is distributed on an "AS IS" BASIS, WITHOUT
+ *  WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ *  See the License for the specific language governing permissions and
+ *  limitations under the License.
+ *
+ *  This file is part of mbed TLS (https://tls.mbed.org)
+ *
+ */
+
+#if !defined(MBEDTLS_CONFIG_FILE)
+#include "mbedtls/config.h"
+#else
+#include MBEDTLS_CONFIG_FILE
+#endif
+
+#if defined(MBEDTLS_RSA_C)
+
+#include "mbedtls/rsa.h"
+#include "mbedtls/bignum.h"
+#include "mbedtls/rsa_internal.h"
+
+/*
+ * Compute RSA prime factors from public and private exponents
+ *
+ * Summary of algorithm:
+ * Setting F := lcm(P-1,Q-1), the idea is as follows:
+ *
+ * (a) For any 1 <= X < N with gcd(X,N)=1, we have X^F = 1 modulo N, so X^(F/2)
+ *     is a square root of 1 in Z/NZ. Since Z/NZ ~= Z/PZ x Z/QZ by CRT and the
+ *     square roots of 1 in Z/PZ and Z/QZ are +1 and -1, this leaves the four
+ *     possibilities X^(F/2) = (+-1, +-1). If it happens that X^(F/2) = (-1,+1)
+ *     or (+1,-1), then gcd(X^(F/2) + 1, N) will be equal to one of the prime
+ *     factors of N.
+ *
+ * (b) If we don't know F/2 but (F/2) * K for some odd (!) K, then the same
+ *     construction still applies since (-)^K is the identity on the set of
+ *     roots of 1 in Z/NZ.
+ *
+ * The public and private key primitives (-)^E and (-)^D are mutually inverse
+ * bijections on Z/NZ if and only if (-)^(DE) is the identity on Z/NZ, i.e.
+ * if and only if DE - 1 is a multiple of F, say DE - 1 = F * L.
+ * Splitting L = 2^t * K with K odd, we have
+ *
+ *   DE - 1 = FL = (F/2) * (2^(t+1)) * K,
+ *
+ * so (F / 2) * K is among the numbers
+ *
+ *   (DE - 1) >> 1, (DE - 1) >> 2, ..., (DE - 1) >> ord
+ *
+ * where ord is the order of 2 in (DE - 1).
+ * We can therefore iterate through these numbers apply the construction
+ * of (a) and (b) above to attempt to factor N.
+ *
+ */
+int mbedtls_rsa_deduce_primes( mbedtls_mpi const *N,
+                     mbedtls_mpi const *E, mbedtls_mpi const *D,
+                     mbedtls_mpi *P, mbedtls_mpi *Q )
+{
+    int ret = 0;
+
+    uint16_t attempt;  /* Number of current attempt  */
+    uint16_t iter;     /* Number of squares computed in the current attempt */
+
+    uint16_t order;    /* Order of 2 in DE - 1 */
+
+    mbedtls_mpi T;  /* Holds largest odd divisor of DE - 1     */
+    mbedtls_mpi K;  /* Temporary holding the current candidate */
+
+    const unsigned char primes[] = { 2,
+           3,    5,    7,   11,   13,   17,   19,   23,
+          29,   31,   37,   41,   43,   47,   53,   59,
+          61,   67,   71,   73,   79,   83,   89,   97,
+         101,  103,  107,  109,  113,  127,  131,  137,
+         139,  149,  151,  157,  163,  167,  173,  179,
+         181,  191,  193,  197,  199,  211,  223,  227,
+         229,  233,  239,  241,  251
+    };
+
+    const size_t num_primes = sizeof( primes ) / sizeof( *primes );
+
+    if( P == NULL || Q == NULL || P->p != NULL || Q->p != NULL )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    if( mbedtls_mpi_cmp_int( N, 0 ) <= 0 ||
+        mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
+        mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
+        mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
+        mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
+    {
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+    }
+
+    /*
+     * Initializations and temporary changes
+     */
+
+    mbedtls_mpi_init( &K );
+    mbedtls_mpi_init( &T );
+
+    /* T := DE - 1 */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &T, D,  E ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &T, &T, 1 ) );
+
+    if( ( order = (uint16_t) mbedtls_mpi_lsb( &T ) ) == 0 )
+    {
+        ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
+        goto cleanup;
+    }
+
+    /* After this operation, T holds the largest odd divisor of DE - 1. */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &T, order ) );
+
+    /*
+     * Actual work
+     */
+
+    /* Skip trying 2 if N == 1 mod 8 */
+    attempt = 0;
+    if( N->p[0] % 8 == 1 )
+        attempt = 1;
+
+    for( ; attempt < num_primes; ++attempt )
+    {
+        mbedtls_mpi_lset( &K, primes[attempt] );
+
+        /* Check if gcd(K,N) = 1 */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
+        if( mbedtls_mpi_cmp_int( P, 1 ) != 0 )
+            continue;
+
+        /* Go through K^T + 1, K^(2T) + 1, K^(4T) + 1, ...
+         * and check whether they have nontrivial GCD with N. */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &K, &K, &T, N,
+                             Q /* temporarily use Q for storing Montgomery
+                                * multiplication helper values */ ) );
+
+        for( iter = 1; iter <= order; ++iter )
+        {
+            /* If we reach 1 prematurely, there's no point
+             * in continuing to square K */
+            if( mbedtls_mpi_cmp_int( &K, 1 ) == 0 )
+                break;
+
+            MBEDTLS_MPI_CHK( mbedtls_mpi_add_int( &K, &K, 1 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( P, &K, N ) );
+
+            if( mbedtls_mpi_cmp_int( P, 1 ) ==  1 &&
+                mbedtls_mpi_cmp_mpi( P, N ) == -1 )
+            {
+                /*
+                 * Have found a nontrivial divisor P of N.
+                 * Set Q := N / P.
+                 */
+
+                MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( Q, NULL, N, P ) );
+                goto cleanup;
+            }
+
+            MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &K ) );
+            MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, N ) );
+        }
+
+        /*
+         * If we get here, then either we prematurely aborted the loop because
+         * we reached 1, or K holds primes[attempt]^(DE - 1) mod N, which must
+         * be 1 if D,E,N were consistent.
+         * Check if that's the case and abort if not, to avoid very long,
+         * yet eventually failing, computations if N,D,E were not sane.
+         */
+        if( mbedtls_mpi_cmp_int( &K, 1 ) != 0 )
+        {
+            break;
+        }
+    }
+
+    ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
+
+cleanup:
+
+    mbedtls_mpi_free( &K );
+    mbedtls_mpi_free( &T );
+    return( ret );
+}
+
+/*
+ * Given P, Q and the public exponent E, deduce D.
+ * This is essentially a modular inversion.
+ */
+int mbedtls_rsa_deduce_private_exponent( mbedtls_mpi const *P,
+                                         mbedtls_mpi const *Q,
+                                         mbedtls_mpi const *E,
+                                         mbedtls_mpi *D )
+{
+    int ret = 0;
+    mbedtls_mpi K, L;
+
+    if( D == NULL || mbedtls_mpi_cmp_int( D, 0 ) != 0 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
+    if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
+        mbedtls_mpi_cmp_int( Q, 1 ) <= 0 ||
+        mbedtls_mpi_cmp_int( E, 0 ) == 0 )
+    {
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+    }
+
+    mbedtls_mpi_init( &K );
+    mbedtls_mpi_init( &L );
+
+    /* Temporarily put K := P-1 and L := Q-1 */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
+
+    /* Temporarily put D := gcd(P-1, Q-1) */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_gcd( D, &K, &L ) );
+
+    /* K := LCM(P-1, Q-1) */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, &K, &L ) );
+    MBEDTLS_MPI_CHK( mbedtls_mpi_div_mpi( &K, NULL, &K, D ) );
+
+    /* Compute modular inverse of E in LCM(P-1, Q-1) */
+    MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( D, E, &K ) );
+
+cleanup:
+
+    mbedtls_mpi_free( &K );
+    mbedtls_mpi_free( &L );
+
+    return( ret );
+}
+
+/*
+ * Check that RSA CRT parameters are in accordance with core parameters.
+ */
+int mbedtls_rsa_validate_crt( const mbedtls_mpi *P,  const mbedtls_mpi *Q,
+                              const mbedtls_mpi *D,  const mbedtls_mpi *DP,
+                              const mbedtls_mpi *DQ, const mbedtls_mpi *QP )
+{
+    int ret = 0;
+
+    mbedtls_mpi K, L;
+    mbedtls_mpi_init( &K );
+    mbedtls_mpi_init( &L );
+
+    /* Check that DP - D == 0 mod P - 1 */
+    if( DP != NULL )
+    {
+        if( P == NULL )
+        {
+            ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
+            goto cleanup;
+        }
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DP, D ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
+
+        if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
+        {
+            ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+            goto cleanup;
+        }
+    }
+
+    /* Check that DQ - D == 0 mod Q - 1 */
+    if( DQ != NULL )
+    {
+        if( Q == NULL )
+        {
+            ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
+            goto cleanup;
+        }
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_mpi( &L, DQ, D ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &L, &L, &K ) );
+
+        if( mbedtls_mpi_cmp_int( &L, 0 ) != 0 )
+        {
+            ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+            goto cleanup;
+        }
+    }
+
+    /* Check that QP * Q - 1 == 0 mod P */
+    if( QP != NULL )
+    {
+        if( P == NULL || Q == NULL )
+        {
+            ret = MBEDTLS_ERR_RSA_BAD_INPUT_DATA;
+            goto cleanup;
+        }
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, QP, Q ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, P ) );
+        if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
+        {
+            ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+            goto cleanup;
+        }
+    }
+
+cleanup:
+
+    /* Wrap MPI error codes by RSA check failure error code */
+    if( ret != 0 &&
+        ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED &&
+        ret != MBEDTLS_ERR_RSA_BAD_INPUT_DATA )
+    {
+        ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+    }
+
+    mbedtls_mpi_free( &K );
+    mbedtls_mpi_free( &L );
+
+    return( ret );
+}
+
+/*
+ * Check that core RSA parameters are sane.
+ */
+int mbedtls_rsa_validate_params( const mbedtls_mpi *N, const mbedtls_mpi *P,
+                                 const mbedtls_mpi *Q, const mbedtls_mpi *D,
+                                 const mbedtls_mpi *E,
+                                 int (*f_rng)(void *, unsigned char *, size_t),
+                                 void *p_rng )
+{
+    int ret = 0;
+    mbedtls_mpi K, L;
+
+    mbedtls_mpi_init( &K );
+    mbedtls_mpi_init( &L );
+
+    /*
+     * Step 1: If PRNG provided, check that P and Q are prime
+     */
+
+#if defined(MBEDTLS_GENPRIME)
+    if( f_rng != NULL && P != NULL &&
+        ( ret = mbedtls_mpi_is_prime( P, f_rng, p_rng ) ) != 0 )
+    {
+        ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+        goto cleanup;
+    }
+
+    if( f_rng != NULL && Q != NULL &&
+        ( ret = mbedtls_mpi_is_prime( Q, f_rng, p_rng ) ) != 0 )
+    {
+        ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+        goto cleanup;
+    }
+#else
+    ((void) f_rng);
+    ((void) p_rng);
+#endif /* MBEDTLS_GENPRIME */
+
+    /*
+     * Step 2: Check that 1 < N = P * Q
+     */
+
+    if( P != NULL && Q != NULL && N != NULL )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, P, Q ) );
+        if( mbedtls_mpi_cmp_int( N, 1 )  <= 0 ||
+            mbedtls_mpi_cmp_mpi( &K, N ) != 0 )
+        {
+            ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+            goto cleanup;
+        }
+    }
+
+    /*
+     * Step 3: Check and 1 < D, E < N if present.
+     */
+
+    if( N != NULL && D != NULL && E != NULL )
+    {
+        if ( mbedtls_mpi_cmp_int( D, 1 ) <= 0 ||
+             mbedtls_mpi_cmp_int( E, 1 ) <= 0 ||
+             mbedtls_mpi_cmp_mpi( D, N ) >= 0 ||
+             mbedtls_mpi_cmp_mpi( E, N ) >= 0 )
+        {
+            ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+            goto cleanup;
+        }
+    }
+
+    /*
+     * Step 4: Check that D, E are inverse modulo P-1 and Q-1
+     */
+
+    if( P != NULL && Q != NULL && D != NULL && E != NULL )
+    {
+        if( mbedtls_mpi_cmp_int( P, 1 ) <= 0 ||
+            mbedtls_mpi_cmp_int( Q, 1 ) <= 0 )
+        {
+            ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+            goto cleanup;
+        }
+
+        /* Compute DE-1 mod P-1 */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, P, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
+        if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
+        {
+            ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+            goto cleanup;
+        }
+
+        /* Compute DE-1 mod Q-1 */
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &K, D, E ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, &K, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &L, Q, 1 ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &K, &K, &L ) );
+        if( mbedtls_mpi_cmp_int( &K, 0 ) != 0 )
+        {
+            ret = MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+            goto cleanup;
+        }
+    }
+
+cleanup:
+
+    mbedtls_mpi_free( &K );
+    mbedtls_mpi_free( &L );
+
+    /* Wrap MPI error codes by RSA check failure error code */
+    if( ret != 0 && ret != MBEDTLS_ERR_RSA_KEY_CHECK_FAILED )
+    {
+        ret += MBEDTLS_ERR_RSA_KEY_CHECK_FAILED;
+    }
+
+    return( ret );
+}
+
+int mbedtls_rsa_deduce_crt( const mbedtls_mpi *P, const mbedtls_mpi *Q,
+                            const mbedtls_mpi *D, mbedtls_mpi *DP,
+                            mbedtls_mpi *DQ, mbedtls_mpi *QP )
+{
+    int ret = 0;
+    mbedtls_mpi K;
+    mbedtls_mpi_init( &K );
+
+    /* DP = D mod P-1 */
+    if( DP != NULL )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, P, 1  ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DP, D, &K ) );
+    }
+
+    /* DQ = D mod Q-1 */
+    if( DQ != NULL )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &K, Q, 1  ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( DQ, D, &K ) );
+    }
+
+    /* QP = Q^{-1} mod P */
+    if( QP != NULL )
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_inv_mod( QP, Q, P ) );
+    }
+
+cleanup:
+    mbedtls_mpi_free( &K );
+
+    return( ret );
+}
+
+#endif /* MBEDTLS_RSA_C */

library/version_features.c

@@ -108,9 +108,6 @@ static const char *features[] = {
 #if defined(MBEDTLS_GCM_ALT)
     "MBEDTLS_GCM_ALT",
 #endif /* MBEDTLS_GCM_ALT */
-#if defined(MBEDTLS_XTEA_ALT)
-    "MBEDTLS_XTEA_ALT",
-#endif /* MBEDTLS_XTEA_ALT */
 #if defined(MBEDTLS_MD2_ALT)
     "MBEDTLS_MD2_ALT",
 #endif /* MBEDTLS_MD2_ALT */
@@ -123,6 +120,9 @@ static const char *features[] = {
 #if defined(MBEDTLS_RIPEMD160_ALT)
     "MBEDTLS_RIPEMD160_ALT",
 #endif /* MBEDTLS_RIPEMD160_ALT */
+#if defined(MBEDTLS_RSA_ALT)
+    "MBEDTLS_RSA_ALT",
+#endif /* MBEDTLS_RSA_ALT */
 #if defined(MBEDTLS_SHA1_ALT)
     "MBEDTLS_SHA1_ALT",
 #endif /* MBEDTLS_SHA1_ALT */
@@ -132,6 +132,9 @@ static const char *features[] = {
 #if defined(MBEDTLS_SHA512_ALT)
     "MBEDTLS_SHA512_ALT",
 #endif /* MBEDTLS_SHA512_ALT */
+#if defined(MBEDTLS_XTEA_ALT)
+    "MBEDTLS_XTEA_ALT",
+#endif /* MBEDTLS_XTEA_ALT */
 #if defined(MBEDTLS_ECP_ALT)
     "MBEDTLS_ECP_ALT",
 #endif /* MBEDTLS_ECP_ALT */

programs/pkey/dh_server.c

@@ -86,6 +86,8 @@ int main( void )
     mbedtls_dhm_context dhm;
     mbedtls_aes_context aes;
 
+    mbedtls_mpi N, P, Q, D, E;
+
     mbedtls_net_init( &listen_fd );
     mbedtls_net_init( &client_fd );
     mbedtls_rsa_init( &rsa, MBEDTLS_RSA_PKCS_V15, MBEDTLS_MD_SHA256 );
@@ -93,6 +95,9 @@ int main( void )
     mbedtls_aes_init( &aes );
     mbedtls_ctr_drbg_init( &ctr_drbg );
 
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P ); mbedtls_mpi_init( &Q );
+    mbedtls_mpi_init( &D ); mbedtls_mpi_init( &E );
+
     /*
      * 1. Setup the RNG
      */
@@ -124,24 +129,33 @@ int main( void )
 
     mbedtls_rsa_init( &rsa, MBEDTLS_RSA_PKCS_V15, 0 );
 
-    if( ( ret = mbedtls_mpi_read_file( &rsa.N , 16, f ) ) != 0 ||
+    if( ( ret = mbedtls_mpi_read_file( &N , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.E , 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &E , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.D , 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &D , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.P , 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &P , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.Q , 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &Q , 16, f ) ) != 0 )
-        ( ret = mbedtls_mpi_read_file( &rsa.DP, 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.DQ, 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.QP, 16, f ) ) != 0 )
     {
-        mbedtls_printf( " failed\n  ! mbedtls_mpi_read_file returned %d\n\n", ret );
+        mbedtls_printf( " failed\n  ! mbedtls_mpi_read_file returned %d\n\n",
+                        ret );
         fclose( f );
         goto exit;
     }
-
-    rsa.len = ( mbedtls_mpi_bitlen( &rsa.N ) + 7 ) >> 3;
-
     fclose( f );
 
+    if( ( ret = mbedtls_rsa_import( &rsa, &N, &P, &Q, &D, &E ) ) != 0 )
+    {
+        mbedtls_printf( " failed\n  ! mbedtls_rsa_import returned %d\n\n",
+                        ret );
+        goto exit;
+    }
+
+    if( ( ret = mbedtls_rsa_complete( &rsa ) ) != 0 )
+    {
+        mbedtls_printf( " failed\n  ! mbedtls_rsa_complete returned %d\n\n",
+                        ret );
+        goto exit;
+    }
+
     /*
      * 2b. Get the DHM modulus and generator
      */
@@ -287,6 +301,9 @@ int main( void )
 
 exit:
 
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P ); mbedtls_mpi_free( &Q );
+    mbedtls_mpi_free( &D ); mbedtls_mpi_free( &E );
+
     mbedtls_net_free( &client_fd );
     mbedtls_net_free( &listen_fd );
 

programs/pkey/gen_key.c

@@ -191,6 +191,7 @@ int main( int argc, char *argv[] )
     char buf[1024];
     int i;
     char *p, *q;
+    mbedtls_mpi N, P, Q, D, E, DP, DQ, QP;
     mbedtls_entropy_context entropy;
     mbedtls_ctr_drbg_context ctr_drbg;
     const char *pers = "gen_key";
@@ -201,6 +202,11 @@ int main( int argc, char *argv[] )
     /*
      * Set to sane values
      */
+
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P ); mbedtls_mpi_init( &Q );
+    mbedtls_mpi_init( &D ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &DP );
+    mbedtls_mpi_init( &DQ ); mbedtls_mpi_init( &QP );
+
     mbedtls_pk_init( &key );
     mbedtls_ctr_drbg_init( &ctr_drbg );
     memset( buf, 0, sizeof( buf ) );
@@ -323,7 +329,7 @@ int main( int argc, char *argv[] )
     if( opt.type == MBEDTLS_PK_RSA )
     {
         ret = mbedtls_rsa_gen_key( mbedtls_pk_rsa( key ), mbedtls_ctr_drbg_random, &ctr_drbg,
-                           opt.rsa_keysize, 65537 );
+                                   opt.rsa_keysize, 65537 );
         if( ret != 0 )
         {
             mbedtls_printf( " failed\n  !  mbedtls_rsa_gen_key returned -0x%04x", -ret );
@@ -336,7 +342,7 @@ int main( int argc, char *argv[] )
     if( opt.type == MBEDTLS_PK_ECKEY )
     {
         ret = mbedtls_ecp_gen_key( opt.ec_curve, mbedtls_pk_ec( key ),
-                          mbedtls_ctr_drbg_random, &ctr_drbg );
+                                   mbedtls_ctr_drbg_random, &ctr_drbg );
         if( ret != 0 )
         {
             mbedtls_printf( " failed\n  !  mbedtls_rsa_gen_key returned -0x%04x", -ret );
@@ -359,14 +365,22 @@ int main( int argc, char *argv[] )
     if( mbedtls_pk_get_type( &key ) == MBEDTLS_PK_RSA )
     {
         mbedtls_rsa_context *rsa = mbedtls_pk_rsa( key );
-        mbedtls_mpi_write_file( "N:  ",  &rsa->N,  16, NULL );
+
-        mbedtls_mpi_write_file( "E:  ",  &rsa->E,  16, NULL );
+        if( ( ret = mbedtls_rsa_export    ( rsa, &N, &P, &Q, &D, &E ) ) != 0 ||
-        mbedtls_mpi_write_file( "D:  ",  &rsa->D,  16, NULL );
+            ( ret = mbedtls_rsa_export_crt( rsa, &DP, &DQ, &QP ) )      != 0 )
-        mbedtls_mpi_write_file( "P:  ",  &rsa->P,  16, NULL );
+        {
-        mbedtls_mpi_write_file( "Q:  ",  &rsa->Q,  16, NULL );
+            mbedtls_printf( " failed\n  ! could not export RSA parameters\n\n" );
-        mbedtls_mpi_write_file( "DP: ",  &rsa->DP, 16, NULL );
+            goto exit;
-        mbedtls_mpi_write_file( "DQ:  ", &rsa->DQ, 16, NULL );
+        }
-        mbedtls_mpi_write_file( "QP:  ", &rsa->QP, 16, NULL );
+
+        mbedtls_mpi_write_file( "N:  ",  &N,  16, NULL );
+        mbedtls_mpi_write_file( "E:  ",  &E,  16, NULL );
+        mbedtls_mpi_write_file( "D:  ",  &D,  16, NULL );
+        mbedtls_mpi_write_file( "P:  ",  &P,  16, NULL );
+        mbedtls_mpi_write_file( "Q:  ",  &Q,  16, NULL );
+        mbedtls_mpi_write_file( "DP: ",  &DP, 16, NULL );
+        mbedtls_mpi_write_file( "DQ:  ", &DQ, 16, NULL );
+        mbedtls_mpi_write_file( "QP:  ", &QP, 16, NULL );
     }
     else
 #endif
@@ -409,6 +423,10 @@ exit:
 #endif
     }
 
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P ); mbedtls_mpi_free( &Q );
+    mbedtls_mpi_free( &D ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &DP );
+    mbedtls_mpi_free( &DQ ); mbedtls_mpi_free( &QP );
+
     mbedtls_pk_free( &key );
     mbedtls_ctr_drbg_free( &ctr_drbg );
     mbedtls_entropy_free( &entropy );
@@ -422,4 +440,3 @@ exit:
 }
 #endif /* MBEDTLS_PK_WRITE_C && MBEDTLS_PEM_WRITE_C && MBEDTLS_FS_IO &&
         * MBEDTLS_ENTROPY_C && MBEDTLS_CTR_DRBG_C */
-

programs/pkey/key_app.c

@@ -84,17 +84,23 @@ struct options
 int main( int argc, char *argv[] )
 {
     int ret = 0;
-    mbedtls_pk_context pk;
     char buf[1024];
     int i;
     char *p, *q;
 
+    mbedtls_pk_context pk;
+    mbedtls_mpi N, P, Q, D, E, DP, DQ, QP;
+
     /*
      * Set to sane values
      */
     mbedtls_pk_init( &pk );
     memset( buf, 0, sizeof(buf) );
 
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P ); mbedtls_mpi_init( &Q );
+    mbedtls_mpi_init( &D ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &DP );
+    mbedtls_mpi_init( &DQ ); mbedtls_mpi_init( &QP );
+
     if( argc == 0 )
     {
     usage:
@@ -189,14 +195,22 @@ int main( int argc, char *argv[] )
         if( mbedtls_pk_get_type( &pk ) == MBEDTLS_PK_RSA )
         {
             mbedtls_rsa_context *rsa = mbedtls_pk_rsa( pk );
-            mbedtls_mpi_write_file( "N:  ", &rsa->N, 16, NULL );
+
-            mbedtls_mpi_write_file( "E:  ", &rsa->E, 16, NULL );
+            if( ( ret = mbedtls_rsa_export    ( rsa, &N, &P, &Q, &D, &E ) ) != 0 ||
-            mbedtls_mpi_write_file( "D:  ", &rsa->D, 16, NULL );
+                ( ret = mbedtls_rsa_export_crt( rsa, &DP, &DQ, &QP ) )      != 0 )
-            mbedtls_mpi_write_file( "P:  ", &rsa->P, 16, NULL );
+            {
-            mbedtls_mpi_write_file( "Q:  ", &rsa->Q, 16, NULL );
+                mbedtls_printf( " failed\n  ! could not export RSA parameters\n\n" );
-            mbedtls_mpi_write_file( "DP: ", &rsa->DP, 16, NULL );
+                goto exit;
-            mbedtls_mpi_write_file( "DQ:  ", &rsa->DQ, 16, NULL );
+            }
-            mbedtls_mpi_write_file( "QP:  ", &rsa->QP, 16, NULL );
+
+            mbedtls_mpi_write_file( "N:  ",  &N,  16, NULL );
+            mbedtls_mpi_write_file( "E:  ",  &E,  16, NULL );
+            mbedtls_mpi_write_file( "D:  ",  &D,  16, NULL );
+            mbedtls_mpi_write_file( "P:  ",  &P,  16, NULL );
+            mbedtls_mpi_write_file( "Q:  ",  &Q,  16, NULL );
+            mbedtls_mpi_write_file( "DP: ",  &DP, 16, NULL );
+            mbedtls_mpi_write_file( "DQ:  ", &DQ, 16, NULL );
+            mbedtls_mpi_write_file( "QP:  ", &QP, 16, NULL );
         }
         else
 #endif
@@ -239,8 +253,15 @@ int main( int argc, char *argv[] )
         if( mbedtls_pk_get_type( &pk ) == MBEDTLS_PK_RSA )
         {
             mbedtls_rsa_context *rsa = mbedtls_pk_rsa( pk );
-            mbedtls_mpi_write_file( "N:  ", &rsa->N, 16, NULL );
+
-            mbedtls_mpi_write_file( "E:  ", &rsa->E, 16, NULL );
+            if( ( ret = mbedtls_rsa_export( rsa, &N, NULL, NULL,
+                                            NULL, &E ) ) != 0 )
+            {
+                mbedtls_printf( " failed\n  ! could not export RSA parameters\n\n" );
+                goto exit;
+            }
+            mbedtls_mpi_write_file( "N: ", &N, 16, NULL );
+            mbedtls_mpi_write_file( "E: ", &E, 16, NULL );
         }
         else
 #endif
@@ -265,11 +286,17 @@ int main( int argc, char *argv[] )
 exit:
 
 #if defined(MBEDTLS_ERROR_C)
-    mbedtls_strerror( ret, buf, sizeof(buf) );
+    if( ret != 0 )
-    mbedtls_printf( "  !  Last error was: %s\n", buf );
+    {
+        mbedtls_strerror( ret, buf, sizeof(buf) );
+        mbedtls_printf( "  !  Last error was: %s\n", buf );
+    }
 #endif
 
     mbedtls_pk_free( &pk );
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P ); mbedtls_mpi_free( &Q );
+    mbedtls_mpi_free( &D ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &DP );
+    mbedtls_mpi_free( &DQ ); mbedtls_mpi_free( &QP );
 
 #if defined(_WIN32)
     mbedtls_printf( "  + Press Enter to exit this program.\n" );

programs/pkey/key_app_writer.c

@@ -76,7 +76,7 @@
 #define OUTPUT_FORMAT_DER              1
 
 #define USAGE \
-    "\n usage: key_app param=<>...\n"                   \
+    "\n usage: key_app_writer param=<>...\n"            \
     "\n acceptable parameters:\n"                       \
     "    mode=private|public default: none\n"           \
     "    filename=%%s         default: keyfile.key\n"   \
@@ -190,17 +190,23 @@ static int write_private_key( mbedtls_pk_context *key, const char *output_file )
 int main( int argc, char *argv[] )
 {
     int ret = 0;
-    mbedtls_pk_context key;
     char buf[1024];
     int i;
     char *p, *q;
 
+    mbedtls_pk_context key;
+    mbedtls_mpi N, P, Q, D, E, DP, DQ, QP;
+
     /*
      * Set to sane values
      */
     mbedtls_pk_init( &key );
     memset( buf, 0, sizeof( buf ) );
 
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P ); mbedtls_mpi_init( &Q );
+    mbedtls_mpi_init( &D ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &DP );
+    mbedtls_mpi_init( &DQ ); mbedtls_mpi_init( &QP );
+
     if( argc == 0 )
     {
     usage:
@@ -300,14 +306,22 @@ int main( int argc, char *argv[] )
         if( mbedtls_pk_get_type( &key ) == MBEDTLS_PK_RSA )
         {
             mbedtls_rsa_context *rsa = mbedtls_pk_rsa( key );
-            mbedtls_mpi_write_file( "N:  ",  &rsa->N,  16, NULL );
+
-            mbedtls_mpi_write_file( "E:  ",  &rsa->E,  16, NULL );
+            if( ( ret = mbedtls_rsa_export    ( rsa, &N, &P, &Q, &D, &E ) ) != 0 ||
-            mbedtls_mpi_write_file( "D:  ",  &rsa->D,  16, NULL );
+                ( ret = mbedtls_rsa_export_crt( rsa, &DP, &DQ, &QP ) )      != 0 )
-            mbedtls_mpi_write_file( "P:  ",  &rsa->P,  16, NULL );
+            {
-            mbedtls_mpi_write_file( "Q:  ",  &rsa->Q,  16, NULL );
+                mbedtls_printf( " failed\n  ! could not export RSA parameters\n\n" );
-            mbedtls_mpi_write_file( "DP: ",  &rsa->DP, 16, NULL );
+                goto exit;
-            mbedtls_mpi_write_file( "DQ:  ", &rsa->DQ, 16, NULL );
+            }
-            mbedtls_mpi_write_file( "QP:  ", &rsa->QP, 16, NULL );
+
+            mbedtls_mpi_write_file( "N:  ",  &N,  16, NULL );
+            mbedtls_mpi_write_file( "E:  ",  &E,  16, NULL );
+            mbedtls_mpi_write_file( "D:  ",  &D,  16, NULL );
+            mbedtls_mpi_write_file( "P:  ",  &P,  16, NULL );
+            mbedtls_mpi_write_file( "Q:  ",  &Q,  16, NULL );
+            mbedtls_mpi_write_file( "DP: ",  &DP, 16, NULL );
+            mbedtls_mpi_write_file( "DQ:  ", &DQ, 16, NULL );
+            mbedtls_mpi_write_file( "QP:  ", &QP, 16, NULL );
         }
         else
 #endif
@@ -353,8 +367,15 @@ int main( int argc, char *argv[] )
         if( mbedtls_pk_get_type( &key ) == MBEDTLS_PK_RSA )
         {
             mbedtls_rsa_context *rsa = mbedtls_pk_rsa( key );
-            mbedtls_mpi_write_file( "N: ", &rsa->N, 16, NULL );
+
-            mbedtls_mpi_write_file( "E: ", &rsa->E, 16, NULL );
+            if( ( ret = mbedtls_rsa_export( rsa, &N, NULL, NULL,
+                                            NULL, &E ) ) != 0 )
+            {
+                mbedtls_printf( " failed\n  ! could not export RSA parameters\n\n" );
+                goto exit;
+            }
+            mbedtls_mpi_write_file( "N: ", &N, 16, NULL );
+            mbedtls_mpi_write_file( "E: ", &E, 16, NULL );
         }
         else
 #endif
@@ -394,6 +415,10 @@ exit:
 #endif
     }
 
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P ); mbedtls_mpi_free( &Q );
+    mbedtls_mpi_free( &D ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &DP );
+    mbedtls_mpi_free( &DQ ); mbedtls_mpi_free( &QP );
+
     mbedtls_pk_free( &key );
 
 #if defined(_WIN32)

programs/pkey/rsa_decrypt.c

@@ -64,6 +64,7 @@ int main( int argc, char *argv[] )
     int return_val, exit_val, c;
     size_t i;
     mbedtls_rsa_context rsa;
+    mbedtls_mpi N, P, Q, D, E, DP, DQ, QP;
     mbedtls_entropy_context entropy;
     mbedtls_ctr_drbg_context ctr_drbg;
     unsigned char result[1024];
@@ -91,6 +92,9 @@ int main( int argc, char *argv[] )
     mbedtls_rsa_init( &rsa, MBEDTLS_RSA_PKCS_V15, 0 );
     mbedtls_ctr_drbg_init( &ctr_drbg );
     mbedtls_entropy_init( &entropy );
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P ); mbedtls_mpi_init( &Q );
+    mbedtls_mpi_init( &D ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &DP );
+    mbedtls_mpi_init( &DQ ); mbedtls_mpi_init( &QP );
 
     return_val = mbedtls_ctr_drbg_seed( &ctr_drbg, mbedtls_entropy_func,
                                         &entropy, (const unsigned char *) pers,
@@ -114,14 +118,14 @@ int main( int argc, char *argv[] )
         goto exit;
     }
 
-    if( ( return_val = mbedtls_mpi_read_file( &rsa.N , 16, f ) ) != 0 ||
+    if( ( return_val = mbedtls_mpi_read_file( &N , 16, f ) )  != 0 ||
-        ( return_val = mbedtls_mpi_read_file( &rsa.E , 16, f ) ) != 0 ||
+        ( return_val = mbedtls_mpi_read_file( &E , 16, f ) )  != 0 ||
-        ( return_val = mbedtls_mpi_read_file( &rsa.D , 16, f ) ) != 0 ||
+        ( return_val = mbedtls_mpi_read_file( &D , 16, f ) )  != 0 ||
-        ( return_val = mbedtls_mpi_read_file( &rsa.P , 16, f ) ) != 0 ||
+        ( return_val = mbedtls_mpi_read_file( &P , 16, f ) )  != 0 ||
-        ( return_val = mbedtls_mpi_read_file( &rsa.Q , 16, f ) ) != 0 ||
+        ( return_val = mbedtls_mpi_read_file( &Q , 16, f ) )  != 0 ||
-        ( return_val = mbedtls_mpi_read_file( &rsa.DP, 16, f ) ) != 0 ||
+        ( return_val = mbedtls_mpi_read_file( &DP , 16, f ) ) != 0 ||
-        ( return_val = mbedtls_mpi_read_file( &rsa.DQ, 16, f ) ) != 0 ||
+        ( return_val = mbedtls_mpi_read_file( &DQ , 16, f ) ) != 0 ||
-        ( return_val = mbedtls_mpi_read_file( &rsa.QP, 16, f ) ) != 0 )
+        ( return_val = mbedtls_mpi_read_file( &QP , 16, f ) ) != 0 )
     {
         exit_val = MBEDTLS_EXIT_FAILURE;
         mbedtls_printf( " failed\n  ! mbedtls_mpi_read_file returned %d\n\n",
@@ -129,11 +133,22 @@ int main( int argc, char *argv[] )
         fclose( f );
         goto exit;
     }
-
-    rsa.len = ( mbedtls_mpi_bitlen( &rsa.N ) + 7 ) >> 3;
-
     fclose( f );
 
+    if( ( return_val = mbedtls_rsa_import( &rsa, &N, &P, &Q, &D, &E ) ) != 0 )
+    {
+        mbedtls_printf( " failed\n  ! mbedtls_rsa_import returned %d\n\n",
+                        return_val );
+        goto exit;
+    }
+
+    if( ( return_val = mbedtls_rsa_complete( &rsa ) ) != 0 )
+    {
+        mbedtls_printf( " failed\n  ! mbedtls_rsa_complete returned %d\n\n",
+                        return_val );
+        goto exit;
+    }
+
     /*
      * Extract the RSA encrypted value from the text file
      */
@@ -184,6 +199,9 @@ exit:
     mbedtls_ctr_drbg_free( &ctr_drbg );
     mbedtls_entropy_free( &entropy );
     mbedtls_rsa_free( &rsa );
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P ); mbedtls_mpi_free( &Q );
+    mbedtls_mpi_free( &D ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &DP );
+    mbedtls_mpi_free( &DQ ); mbedtls_mpi_free( &QP );
 
 #if defined(_WIN32)
     mbedtls_printf( "  + Press Enter to exit this program.\n" );
@@ -193,4 +211,3 @@ exit:
     return( exit_val );
 }
 #endif /* MBEDTLS_BIGNUM_C && MBEDTLS_RSA_C && MBEDTLS_FS_IO */
-

programs/pkey/rsa_encrypt.c

@@ -69,6 +69,7 @@ int main( int argc, char *argv[] )
     unsigned char input[1024];
     unsigned char buf[512];
     const char *pers = "rsa_encrypt";
+    mbedtls_mpi N, E;
 
     exit_val = MBEDTLS_EXIT_SUCCESS;
 
@@ -86,6 +87,7 @@ int main( int argc, char *argv[] )
     mbedtls_printf( "\n  . Seeding the random number generator..." );
     fflush( stdout );
 
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &E );
     mbedtls_rsa_init( &rsa, MBEDTLS_RSA_PKCS_V15, 0 );
     mbedtls_ctr_drbg_init( &ctr_drbg );
     mbedtls_entropy_init( &entropy );
@@ -112,8 +114,8 @@ int main( int argc, char *argv[] )
         goto exit;
     }
 
-    if( ( return_val = mbedtls_mpi_read_file( &rsa.N, 16, f ) ) != 0 ||
+    if( ( return_val = mbedtls_mpi_read_file( &N, 16, f ) ) != 0 ||
-        ( return_val = mbedtls_mpi_read_file( &rsa.E, 16, f ) ) != 0 )
+        ( return_val = mbedtls_mpi_read_file( &E, 16, f ) ) != 0 )
     {
         exit_val = MBEDTLS_EXIT_FAILURE;
         mbedtls_printf( " failed\n  ! mbedtls_mpi_read_file returned %d\n\n",
@@ -121,11 +123,17 @@ int main( int argc, char *argv[] )
         fclose( f );
         goto exit;
     }
-
-    rsa.len = ( mbedtls_mpi_bitlen( &rsa.N ) + 7 ) >> 3;
-
     fclose( f );
 
+    if( ( return_val = mbedtls_rsa_import( &rsa, &N, NULL,
+                                           NULL, NULL, &E ) ) != 0 )
+    {
+        exit_val = MBEDTLS_EXIT_FAILURE;
+        mbedtls_printf( " failed\n  ! mbedtls_rsa_import returned %d\n\n",
+                        return_val );
+        goto exit;
+    }
+
     if( strlen( argv[1] ) > 100 )
     {
         exit_val = MBEDTLS_EXIT_FAILURE;
@@ -171,6 +179,7 @@ int main( int argc, char *argv[] )
     mbedtls_printf( "\n  . Done (created \"%s\")\n\n", "result-enc.txt" );
 
 exit:
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &E );
     mbedtls_ctr_drbg_free( &ctr_drbg );
     mbedtls_entropy_free( &entropy );
     mbedtls_rsa_free( &rsa );

programs/pkey/rsa_genkey.c

@@ -65,6 +65,7 @@ int main( void )
     mbedtls_rsa_context rsa;
     mbedtls_entropy_context entropy;
     mbedtls_ctr_drbg_context ctr_drbg;
+    mbedtls_mpi N, P, Q, D, E, DP, DQ, QP;
     FILE *fpub  = NULL;
     FILE *fpriv = NULL;
     const char *pers = "rsa_genkey";
@@ -87,9 +88,12 @@ int main( void )
     fflush( stdout );
 
     mbedtls_rsa_init( &rsa, MBEDTLS_RSA_PKCS_V15, 0 );
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P ); mbedtls_mpi_init( &Q );
+    mbedtls_mpi_init( &D ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &DP );
+    mbedtls_mpi_init( &DQ ); mbedtls_mpi_init( &QP );
 
     if( ( ret = mbedtls_rsa_gen_key( &rsa, mbedtls_ctr_drbg_random, &ctr_drbg, KEY_SIZE,
-                             EXPONENT ) ) != 0 )
+                                     EXPONENT ) ) != 0 )
     {
         mbedtls_printf( " failed\n  ! mbedtls_rsa_gen_key returned %d\n\n", ret );
         goto exit;
@@ -98,6 +102,14 @@ int main( void )
     mbedtls_printf( " ok\n  . Exporting the public  key in rsa_pub.txt...." );
     fflush( stdout );
 
+    if( ( ret = mbedtls_rsa_export    ( &rsa, &N, &P, &Q, &D, &E ) ) != 0 ||
+        ( ret = mbedtls_rsa_export_crt( &rsa, &DP, &DQ, &QP ) )      != 0 )
+    {
+        mbedtls_printf( " failed\n  ! could not export RSA parameters\n\n" );
+        ret = 1;
+        goto exit;
+    }
+
     if( ( fpub = fopen( "rsa_pub.txt", "wb+" ) ) == NULL )
     {
         mbedtls_printf( " failed\n  ! could not open rsa_pub.txt for writing\n\n" );
@@ -105,8 +117,8 @@ int main( void )
         goto exit;
     }
 
-    if( ( ret = mbedtls_mpi_write_file( "N = ", &rsa.N, 16, fpub ) ) != 0 ||
+    if( ( ret = mbedtls_mpi_write_file( "N = ", &N, 16, fpub ) ) != 0 ||
-        ( ret = mbedtls_mpi_write_file( "E = ", &rsa.E, 16, fpub ) ) != 0 )
+        ( ret = mbedtls_mpi_write_file( "E = ", &E, 16, fpub ) ) != 0 )
     {
         mbedtls_printf( " failed\n  ! mbedtls_mpi_write_file returned %d\n\n", ret );
         goto exit;
@@ -122,14 +134,14 @@ int main( void )
         goto exit;
     }
 
-    if( ( ret = mbedtls_mpi_write_file( "N = " , &rsa.N , 16, fpriv ) ) != 0 ||
+    if( ( ret = mbedtls_mpi_write_file( "N = " , &N , 16, fpriv ) ) != 0 ||
-        ( ret = mbedtls_mpi_write_file( "E = " , &rsa.E , 16, fpriv ) ) != 0 ||
+        ( ret = mbedtls_mpi_write_file( "E = " , &E , 16, fpriv ) ) != 0 ||
-        ( ret = mbedtls_mpi_write_file( "D = " , &rsa.D , 16, fpriv ) ) != 0 ||
+        ( ret = mbedtls_mpi_write_file( "D = " , &D , 16, fpriv ) ) != 0 ||
-        ( ret = mbedtls_mpi_write_file( "P = " , &rsa.P , 16, fpriv ) ) != 0 ||
+        ( ret = mbedtls_mpi_write_file( "P = " , &P , 16, fpriv ) ) != 0 ||
-        ( ret = mbedtls_mpi_write_file( "Q = " , &rsa.Q , 16, fpriv ) ) != 0 ||
+        ( ret = mbedtls_mpi_write_file( "Q = " , &Q , 16, fpriv ) ) != 0 ||
-        ( ret = mbedtls_mpi_write_file( "DP = ", &rsa.DP, 16, fpriv ) ) != 0 ||
+        ( ret = mbedtls_mpi_write_file( "DP = ", &DP, 16, fpriv ) ) != 0 ||
-        ( ret = mbedtls_mpi_write_file( "DQ = ", &rsa.DQ, 16, fpriv ) ) != 0 ||
+        ( ret = mbedtls_mpi_write_file( "DQ = ", &DQ, 16, fpriv ) ) != 0 ||
-        ( ret = mbedtls_mpi_write_file( "QP = ", &rsa.QP, 16, fpriv ) ) != 0 )
+        ( ret = mbedtls_mpi_write_file( "QP = ", &QP, 16, fpriv ) ) != 0 )
     {
         mbedtls_printf( " failed\n  ! mbedtls_mpi_write_file returned %d\n\n", ret );
         goto exit;
@@ -157,6 +169,9 @@ exit:
     if( fpriv != NULL )
         fclose( fpriv );
 
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P ); mbedtls_mpi_free( &Q );
+    mbedtls_mpi_free( &D ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &DP );
+    mbedtls_mpi_free( &DQ ); mbedtls_mpi_free( &QP );
     mbedtls_rsa_free( &rsa );
     mbedtls_ctr_drbg_free( &ctr_drbg );
     mbedtls_entropy_free( &entropy );

programs/pkey/rsa_sign.c

@@ -61,8 +61,14 @@ int main( int argc, char *argv[] )
     unsigned char hash[32];
     unsigned char buf[MBEDTLS_MPI_MAX_SIZE];
     char filename[512];
+    mbedtls_mpi N, P, Q, D, E, DP, DQ, QP;
 
     mbedtls_rsa_init( &rsa, MBEDTLS_RSA_PKCS_V15, 0 );
+
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P ); mbedtls_mpi_init( &Q );
+    mbedtls_mpi_init( &D ); mbedtls_mpi_init( &E ); mbedtls_mpi_init( &DP );
+    mbedtls_mpi_init( &DQ ); mbedtls_mpi_init( &QP );
+
     ret = 1;
 
     if( argc != 2 )
@@ -87,24 +93,35 @@ int main( int argc, char *argv[] )
         goto exit;
     }
 
-    if( ( ret = mbedtls_mpi_read_file( &rsa.N , 16, f ) ) != 0 ||
+    if( ( ret = mbedtls_mpi_read_file( &N , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.E , 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &E , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.D , 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &D , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.P , 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &P , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.Q , 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &Q , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.DP, 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &DP , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.DQ, 16, f ) ) != 0 ||
+        ( ret = mbedtls_mpi_read_file( &DQ , 16, f ) ) != 0 ||
-        ( ret = mbedtls_mpi_read_file( &rsa.QP, 16, f ) ) != 0 )
+        ( ret = mbedtls_mpi_read_file( &QP , 16, f ) ) != 0 )
     {
         mbedtls_printf( " failed\n  ! mbedtls_mpi_read_file returned %d\n\n", ret );
         fclose( f );
         goto exit;
     }
-
-    rsa.len = ( mbedtls_mpi_bitlen( &rsa.N ) + 7 ) >> 3;
-
     fclose( f );
 
+    if( ( ret = mbedtls_rsa_import( &rsa, &N, &P, &Q, &D, &E ) ) != 0 )
+    {
+        mbedtls_printf( " failed\n  ! mbedtls_rsa_import returned %d\n\n",
+                        ret );
+        goto exit;
+    }
+
+    if( ( ret = mbedtls_rsa_complete( &rsa ) ) != 0 )
+    {
+        mbedtls_printf( " failed\n  ! mbedtls_rsa_complete returned %d\n\n",
+                        ret );
+        goto exit;
+    }
+
     mbedtls_printf( "\n  . Checking the private key" );
     fflush( stdout );
     if( ( ret = mbedtls_rsa_check_privkey( &rsa ) ) != 0 )
@@ -158,6 +175,9 @@ int main( int argc, char *argv[] )
 exit:
 
     mbedtls_rsa_free( &rsa );
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P ); mbedtls_mpi_free( &Q );
+    mbedtls_mpi_free( &D ); mbedtls_mpi_free( &E ); mbedtls_mpi_free( &DP );
+    mbedtls_mpi_free( &DQ ); mbedtls_mpi_free( &QP );
 
 #if defined(_WIN32)
     mbedtls_printf( "  + Press Enter to exit this program.\n" );

tests/scripts/all.sh

@@ -605,7 +605,7 @@ cleanup
 cp "$CONFIG_H" "$CONFIG_BAK"
 scripts/config.pl full
 scripts/config.pl unset MBEDTLS_SSL_CLI_C
-make CC=gcc CFLAGS='-Werror -Wall -Werror -O0'
+make CC=gcc CFLAGS='-Werror -Wall -Wextra -O0'
 
 # Note, C99 compliance can also be tested with the sockets support disabled,
 # as that requires a POSIX platform (which isn't the same as C99).
@@ -767,6 +767,16 @@ msg "test: allow SHA1 in certificates by default"
 make test
 if_build_succeeded tests/ssl-opt.sh -f SHA-1
 
+msg "build: Default + MBEDTLS_RSA_NO_CRT (ASan build)" # ~ 6 min
+cleanup
+cp "$CONFIG_H" "$CONFIG_BAK"
+scripts/config.pl set MBEDTLS_RSA_NO_CRT
+CC=gcc cmake -D CMAKE_BUILD_TYPE:String=Asan .
+make
+
+msg "test: MBEDTLS_RSA_NO_CRT - main suites (inc. selftests) (ASan build)"
+make test
+
 msg "build: Windows cross build - mingw64, make (Link Library)" # ~ 30s
 cleanup
 make CC=i686-w64-mingw32-gcc AR=i686-w64-mingw32-ar LD=i686-w64-minggw32-ld CFLAGS='-Werror -Wall -Wextra' WINDOWS_BUILD=1 lib programs

tests/suites/test_suite_pk.function

@@ -333,18 +333,19 @@ void pk_rsa_decrypt_test_vec( char *cipher_hex, int mod,
     unsigned char cipher[1000];
     size_t clear_len, olen, cipher_len;
     rnd_pseudo_info rnd_info;
-    mbedtls_mpi P1, Q1, H, G;
+    mbedtls_mpi N, P, Q, E;
     mbedtls_rsa_context *rsa;
     mbedtls_pk_context pk;
 
     mbedtls_pk_init( &pk );
-    mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 ); mbedtls_mpi_init( &H ); mbedtls_mpi_init( &G );
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P );
+    mbedtls_mpi_init( &Q ); mbedtls_mpi_init( &E );
 
     memset( &rnd_info,  0, sizeof( rnd_pseudo_info ) );
     memset( clear,      0, sizeof( clear ) );
     memset( cipher,     0, sizeof( cipher ) );
 
-    clear_len = unhexify( clear, clear_hex );
+    clear_len  = unhexify( clear,   clear_hex );
     cipher_len = unhexify( cipher, cipher_hex );
 
     /* init pk-rsa context */
@@ -352,21 +353,15 @@ void pk_rsa_decrypt_test_vec( char *cipher_hex, int mod,
     rsa = mbedtls_pk_rsa( pk );
 
     /* load public key */
-    rsa->len = mod / 8;
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &rsa->N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &rsa->E, radix_E, input_E ) == 0 );
 
     /* load private key */
-    TEST_ASSERT( mbedtls_mpi_read_string( &rsa->P, radix_P, input_P ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &P, radix_P, input_P ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &rsa->Q, radix_Q, input_Q ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &Q, radix_Q, input_Q ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_sub_int( &P1, &rsa->P, 1 ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_import( rsa, &N, &P, &Q, NULL, &E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_sub_int( &Q1, &rsa->Q, 1 ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_get_len( rsa ) == (size_t) ( mod / 8 ) );
-    TEST_ASSERT( mbedtls_mpi_mul_mpi( &H, &P1, &Q1 ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_complete( rsa ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_gcd( &G, &rsa->E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &rsa->D , &rsa->E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &rsa->DP, &rsa->D, &P1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &rsa->DQ, &rsa->D, &Q1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &rsa->QP, &rsa->Q, &rsa->P ) == 0 );
 
     /* decryption test */
     memset( output, 0, sizeof( output ) );
@@ -381,7 +376,8 @@ void pk_rsa_decrypt_test_vec( char *cipher_hex, int mod,
     }
 
 exit:
-    mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &H ); mbedtls_mpi_free( &G );
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P );
+    mbedtls_mpi_free( &Q ); mbedtls_mpi_free( &E );
     mbedtls_pk_free( &pk );
 }
 /* END_CASE */

tests/suites/test_suite_pkcs1_v15.function

@@ -21,19 +21,21 @@ void pkcs1_rsaes_v15_encrypt( int mod, int radix_N, char *input_N, int radix_E,
     mbedtls_rsa_context ctx;
     size_t msg_len;
     rnd_buf_info info;
+    mbedtls_mpi N, E;
 
     info.length = unhexify( rnd_buf, seed );
     info.buf = rnd_buf;
 
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &E );
     mbedtls_rsa_init( &ctx, MBEDTLS_RSA_PKCS_V15, hash );
     memset( message_str, 0x00, 1000 );
     memset( output, 0x00, 1000 );
     memset( output_str, 0x00, 1000 );
 
-    ctx.len = mod / 8 + ( ( mod % 8 ) ? 1 : 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.E, radix_E, input_E ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_import( &ctx, &N, NULL, NULL, NULL, &E ) == 0 );
-
+    TEST_ASSERT( mbedtls_rsa_get_len( &ctx ) == (size_t) ( ( mod + 7 ) / 8 ) );
     TEST_ASSERT( mbedtls_rsa_check_pubkey( &ctx ) == 0 );
 
     msg_len = unhexify( message_str, message_hex_string );
@@ -47,6 +49,7 @@ void pkcs1_rsaes_v15_encrypt( int mod, int radix_N, char *input_N, int radix_E,
     }
 
 exit:
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &E );
     mbedtls_rsa_free( &ctx );
 }
 /* END_CASE */
@@ -62,12 +65,13 @@ void pkcs1_rsaes_v15_decrypt( int mod, int radix_P, char *input_P,
     unsigned char output[1000];
     unsigned char output_str[1000];
     mbedtls_rsa_context ctx;
-    mbedtls_mpi P1, Q1, H, G;
     size_t output_len;
     rnd_pseudo_info rnd_info;
+    mbedtls_mpi N, P, Q, E;
     ((void) seed);
 
-    mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 ); mbedtls_mpi_init( &H ); mbedtls_mpi_init( &G );
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P );
+    mbedtls_mpi_init( &Q ); mbedtls_mpi_init( &E );
     mbedtls_rsa_init( &ctx, MBEDTLS_RSA_PKCS_V15, hash );
 
     memset( message_str, 0x00, 1000 );
@@ -75,21 +79,14 @@ void pkcs1_rsaes_v15_decrypt( int mod, int radix_P, char *input_P,
     memset( output_str, 0x00, 1000 );
     memset( &rnd_info, 0, sizeof( rnd_pseudo_info ) );
 
-    ctx.len = mod / 8 + ( ( mod % 8 ) ? 1 : 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &P, radix_P, input_P ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.P, radix_P, input_P ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &Q, radix_Q, input_Q ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.Q, radix_Q, input_Q ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.E, radix_E, input_E ) == 0 );
-
-    TEST_ASSERT( mbedtls_mpi_sub_int( &P1, &ctx.P, 1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_sub_int( &Q1, &ctx.Q, 1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mul_mpi( &H, &P1, &Q1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_gcd( &G, &ctx.E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &ctx.D , &ctx.E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &ctx.DP, &ctx.D, &P1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &ctx.DQ, &ctx.D, &Q1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &ctx.QP, &ctx.Q, &ctx.P ) == 0 );
 
+    TEST_ASSERT( mbedtls_rsa_import( &ctx, &N, &P, &Q, NULL, &E ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_get_len( &ctx ) == (size_t) ( ( mod + 7 ) / 8 ) );
+    TEST_ASSERT( mbedtls_rsa_complete( &ctx ) == 0 );
     TEST_ASSERT( mbedtls_rsa_check_privkey( &ctx ) == 0 );
 
     unhexify( message_str, message_hex_string );
@@ -103,7 +100,8 @@ void pkcs1_rsaes_v15_decrypt( int mod, int radix_P, char *input_P,
     }
 
 exit:
-    mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &H ); mbedtls_mpi_free( &G );
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P );
+    mbedtls_mpi_free( &Q ); mbedtls_mpi_free( &E );
     mbedtls_rsa_free( &ctx );
 }
 /* END_CASE */
@@ -121,14 +119,15 @@ void pkcs1_rsassa_v15_sign( int mod, int radix_P, char *input_P, int radix_Q,
     unsigned char output_str[1000];
     unsigned char rnd_buf[1000];
     mbedtls_rsa_context ctx;
-    mbedtls_mpi P1, Q1, H, G;
+    mbedtls_mpi N, P, Q, E;
     size_t msg_len;
     rnd_buf_info info;
 
     info.length = unhexify( rnd_buf, salt );
     info.buf = rnd_buf;
 
-    mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 ); mbedtls_mpi_init( &H ); mbedtls_mpi_init( &G );
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P );
+    mbedtls_mpi_init( &Q ); mbedtls_mpi_init( &E );
     mbedtls_rsa_init( &ctx, MBEDTLS_RSA_PKCS_V15, hash );
 
     memset( message_str, 0x00, 1000 );
@@ -136,21 +135,14 @@ void pkcs1_rsassa_v15_sign( int mod, int radix_P, char *input_P, int radix_Q,
     memset( output, 0x00, 1000 );
     memset( output_str, 0x00, 1000 );
 
-    ctx.len = mod / 8 + ( ( mod % 8 ) ? 1 : 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &P, radix_P, input_P ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.P, radix_P, input_P ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &Q, radix_Q, input_Q ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.Q, radix_Q, input_Q ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.E, radix_E, input_E ) == 0 );
-
-    TEST_ASSERT( mbedtls_mpi_sub_int( &P1, &ctx.P, 1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_sub_int( &Q1, &ctx.Q, 1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mul_mpi( &H, &P1, &Q1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_gcd( &G, &ctx.E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &ctx.D , &ctx.E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &ctx.DP, &ctx.D, &P1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &ctx.DQ, &ctx.D, &Q1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &ctx.QP, &ctx.Q, &ctx.P ) == 0 );
 
+    TEST_ASSERT( mbedtls_rsa_import( &ctx, &N, &P, &Q, NULL, &E ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_get_len( &ctx ) == (size_t) ( ( mod + 7 ) / 8 ) );
+    TEST_ASSERT( mbedtls_rsa_complete( &ctx ) == 0 );
     TEST_ASSERT( mbedtls_rsa_check_privkey( &ctx ) == 0 );
 
     msg_len = unhexify( message_str, message_hex_string );
@@ -167,7 +159,8 @@ void pkcs1_rsassa_v15_sign( int mod, int radix_P, char *input_P, int radix_Q,
     }
 
 exit:
-    mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &H ); mbedtls_mpi_free( &G );
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P );
+    mbedtls_mpi_free( &Q ); mbedtls_mpi_free( &E );
     mbedtls_rsa_free( &ctx );
 }
 /* END_CASE */
@@ -183,28 +176,34 @@ void pkcs1_rsassa_v15_verify( int mod, int radix_N, char *input_N, int radix_E,
     unsigned char result_str[1000];
     mbedtls_rsa_context ctx;
     size_t msg_len;
+    mbedtls_mpi N, E;
     ((void) salt);
 
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &E );
     mbedtls_rsa_init( &ctx, MBEDTLS_RSA_PKCS_V15, hash );
     memset( message_str, 0x00, 1000 );
     memset( hash_result, 0x00, 1000 );
     memset( result_str, 0x00, 1000 );
 
-    ctx.len = mod / 8 + ( ( mod % 8 ) ? 1 : 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.E, radix_E, input_E ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_import( &ctx, &N, NULL, NULL, NULL, &E ) == 0 );
-
+    TEST_ASSERT( mbedtls_rsa_get_len( &ctx ) == (size_t) ( ( mod + 7 ) / 8 ) );
     TEST_ASSERT( mbedtls_rsa_check_pubkey( &ctx ) == 0 );
 
     msg_len = unhexify( message_str, message_hex_string );
     unhexify( result_str, result_hex_str );
 
     if( mbedtls_md_info_from_type( digest ) != NULL )
-        TEST_ASSERT( mbedtls_md( mbedtls_md_info_from_type( digest ), message_str, msg_len, hash_result ) == 0 );
+        TEST_ASSERT( mbedtls_md( mbedtls_md_info_from_type( digest ),
+                                 message_str, msg_len, hash_result ) == 0 );
 
-    TEST_ASSERT( mbedtls_rsa_pkcs1_verify( &ctx, NULL, NULL, MBEDTLS_RSA_PUBLIC, digest, 0, hash_result, result_str ) == result );
+    TEST_ASSERT( mbedtls_rsa_pkcs1_verify( &ctx, NULL, NULL, MBEDTLS_RSA_PUBLIC,
+                                           digest, 0, hash_result,
+                                           result_str ) == result );
 
 exit:
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &E );
     mbedtls_rsa_free( &ctx );
 }
 /* END_CASE */

tests/suites/test_suite_pkcs1_v21.function

@@ -21,19 +21,21 @@ void pkcs1_rsaes_oaep_encrypt( int mod, int radix_N, char *input_N, int radix_E,
     mbedtls_rsa_context ctx;
     size_t msg_len;
     rnd_buf_info info;
+    mbedtls_mpi N, E;
 
     info.length = unhexify( rnd_buf, seed );
     info.buf = rnd_buf;
 
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &E );
     mbedtls_rsa_init( &ctx, MBEDTLS_RSA_PKCS_V21, hash );
     memset( message_str, 0x00, 1000 );
     memset( output, 0x00, 1000 );
     memset( output_str, 0x00, 1000 );
 
-    ctx.len = mod / 8 + ( ( mod % 8 ) ? 1 : 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.E, radix_E, input_E ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_import( &ctx, &N, NULL, NULL, NULL, &E ) == 0 );
-
+    TEST_ASSERT( mbedtls_rsa_get_len( &ctx ) == (size_t) ( ( mod + 7 ) / 8 ) );
     TEST_ASSERT( mbedtls_rsa_check_pubkey( &ctx ) == 0 );
 
     msg_len = unhexify( message_str, message_hex_string );
@@ -47,6 +49,7 @@ void pkcs1_rsaes_oaep_encrypt( int mod, int radix_N, char *input_N, int radix_E,
     }
 
 exit:
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &E );
     mbedtls_rsa_free( &ctx );
 }
 /* END_CASE */
@@ -62,12 +65,14 @@ void pkcs1_rsaes_oaep_decrypt( int mod, int radix_P, char *input_P,
     unsigned char output[1000];
     unsigned char output_str[1000];
     mbedtls_rsa_context ctx;
-    mbedtls_mpi P1, Q1, H, G;
     size_t output_len;
     rnd_pseudo_info rnd_info;
+    mbedtls_mpi N, P, Q, E;
     ((void) seed);
 
-    mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 ); mbedtls_mpi_init( &H ); mbedtls_mpi_init( &G );
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P );
+    mbedtls_mpi_init( &Q ); mbedtls_mpi_init( &E );
+
     mbedtls_rsa_init( &ctx, MBEDTLS_RSA_PKCS_V21, hash );
 
     memset( message_str, 0x00, 1000 );
@@ -75,21 +80,14 @@ void pkcs1_rsaes_oaep_decrypt( int mod, int radix_P, char *input_P,
     memset( output_str, 0x00, 1000 );
     memset( &rnd_info, 0, sizeof( rnd_pseudo_info ) );
 
-    ctx.len = mod / 8 + ( ( mod % 8 ) ? 1 : 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &P, radix_P, input_P ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.P, radix_P, input_P ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &Q, radix_Q, input_Q ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.Q, radix_Q, input_Q ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.E, radix_E, input_E ) == 0 );
-
-    TEST_ASSERT( mbedtls_mpi_sub_int( &P1, &ctx.P, 1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_sub_int( &Q1, &ctx.Q, 1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mul_mpi( &H, &P1, &Q1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_gcd( &G, &ctx.E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &ctx.D , &ctx.E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &ctx.DP, &ctx.D, &P1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &ctx.DQ, &ctx.D, &Q1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &ctx.QP, &ctx.Q, &ctx.P ) == 0 );
 
+    TEST_ASSERT( mbedtls_rsa_import( &ctx, &N, &P, &Q, NULL, &E ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_get_len( &ctx ) == (size_t) ( ( mod + 7 ) / 8 ) );
+    TEST_ASSERT( mbedtls_rsa_complete( &ctx ) == 0 );
     TEST_ASSERT( mbedtls_rsa_check_privkey( &ctx ) == 0 );
 
     unhexify( message_str, message_hex_string );
@@ -103,7 +101,8 @@ void pkcs1_rsaes_oaep_decrypt( int mod, int radix_P, char *input_P,
     }
 
 exit:
-    mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &H ); mbedtls_mpi_free( &G );
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P );
+    mbedtls_mpi_free( &Q ); mbedtls_mpi_free( &E );
     mbedtls_rsa_free( &ctx );
 }
 /* END_CASE */
@@ -121,14 +120,15 @@ void pkcs1_rsassa_pss_sign( int mod, int radix_P, char *input_P, int radix_Q,
     unsigned char output_str[1000];
     unsigned char rnd_buf[1000];
     mbedtls_rsa_context ctx;
-    mbedtls_mpi P1, Q1, H, G;
     size_t msg_len;
     rnd_buf_info info;
+    mbedtls_mpi N, P, Q, E;
 
     info.length = unhexify( rnd_buf, salt );
     info.buf = rnd_buf;
 
-    mbedtls_mpi_init( &P1 ); mbedtls_mpi_init( &Q1 ); mbedtls_mpi_init( &H ); mbedtls_mpi_init( &G );
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &P );
+    mbedtls_mpi_init( &Q ); mbedtls_mpi_init( &E );
     mbedtls_rsa_init( &ctx, MBEDTLS_RSA_PKCS_V21, hash );
 
     memset( message_str, 0x00, 1000 );
@@ -136,29 +136,24 @@ void pkcs1_rsassa_pss_sign( int mod, int radix_P, char *input_P, int radix_Q,
     memset( output, 0x00, 1000 );
     memset( output_str, 0x00, 1000 );
 
-    ctx.len = mod / 8 + ( ( mod % 8 ) ? 1 : 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &P, radix_P, input_P ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.P, radix_P, input_P ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &Q, radix_Q, input_Q ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.Q, radix_Q, input_Q ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.E, radix_E, input_E ) == 0 );
-
-    TEST_ASSERT( mbedtls_mpi_sub_int( &P1, &ctx.P, 1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_sub_int( &Q1, &ctx.Q, 1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mul_mpi( &H, &P1, &Q1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_gcd( &G, &ctx.E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &ctx.D , &ctx.E, &H  ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &ctx.DP, &ctx.D, &P1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_mod_mpi( &ctx.DQ, &ctx.D, &Q1 ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_inv_mod( &ctx.QP, &ctx.Q, &ctx.P ) == 0 );
 
+    TEST_ASSERT( mbedtls_rsa_import( &ctx, &N, &P, &Q, NULL, &E ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_get_len( &ctx ) == (size_t) ( ( mod + 7 ) / 8 ) );
+    TEST_ASSERT( mbedtls_rsa_complete( &ctx ) == 0 );
     TEST_ASSERT( mbedtls_rsa_check_privkey( &ctx ) == 0 );
 
     msg_len = unhexify( message_str, message_hex_string );
 
     if( mbedtls_md_info_from_type( digest ) != NULL )
-        TEST_ASSERT( mbedtls_md( mbedtls_md_info_from_type( digest ), message_str, msg_len, hash_result ) == 0 );
+        TEST_ASSERT( mbedtls_md( mbedtls_md_info_from_type( digest ), message_str,
+                                 msg_len, hash_result ) == 0 );
 
-    TEST_ASSERT( mbedtls_rsa_pkcs1_sign( &ctx, &rnd_buffer_rand, &info, MBEDTLS_RSA_PRIVATE, digest, 0, hash_result, output ) == result );
+    TEST_ASSERT( mbedtls_rsa_pkcs1_sign( &ctx, &rnd_buffer_rand, &info, MBEDTLS_RSA_PRIVATE,
+                                         digest, 0, hash_result, output ) == result );
     if( result == 0 )
     {
         hexify( output_str, output, ctx.len);
@@ -167,7 +162,8 @@ void pkcs1_rsassa_pss_sign( int mod, int radix_P, char *input_P, int radix_Q,
     }
 
 exit:
-    mbedtls_mpi_free( &P1 ); mbedtls_mpi_free( &Q1 ); mbedtls_mpi_free( &H ); mbedtls_mpi_free( &G );
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &P );
+    mbedtls_mpi_free( &Q ); mbedtls_mpi_free( &E );
     mbedtls_rsa_free( &ctx );
 }
 /* END_CASE */
@@ -183,28 +179,34 @@ void pkcs1_rsassa_pss_verify( int mod, int radix_N, char *input_N, int radix_E,
     unsigned char result_str[1000];
     mbedtls_rsa_context ctx;
     size_t msg_len;
+    mbedtls_mpi N, E;
     ((void) salt);
 
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &E );
     mbedtls_rsa_init( &ctx, MBEDTLS_RSA_PKCS_V21, hash );
     memset( message_str, 0x00, 1000 );
     memset( hash_result, 0x00, 1000 );
     memset( result_str, 0x00, 1000 );
 
-    ctx.len = mod / 8 + ( ( mod % 8 ) ? 1 : 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.E, radix_E, input_E ) == 0 );
 
+    TEST_ASSERT( mbedtls_rsa_import( &ctx, &N, NULL, NULL, NULL, &E ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_get_len( &ctx ) == (size_t) ( ( mod + 7 ) / 8 ) );
     TEST_ASSERT( mbedtls_rsa_check_pubkey( &ctx ) == 0 );
 
     msg_len = unhexify( message_str, message_hex_string );
     unhexify( result_str, result_hex_str );
 
     if( mbedtls_md_info_from_type( digest ) != NULL )
-        TEST_ASSERT( mbedtls_md( mbedtls_md_info_from_type( digest ), message_str, msg_len, hash_result ) == 0 );
+        TEST_ASSERT( mbedtls_md( mbedtls_md_info_from_type( digest ), message_str,
+                                 msg_len, hash_result ) == 0 );
 
-    TEST_ASSERT( mbedtls_rsa_pkcs1_verify( &ctx, NULL, NULL, MBEDTLS_RSA_PUBLIC, digest, 0, hash_result, result_str ) == result );
+    TEST_ASSERT( mbedtls_rsa_pkcs1_verify( &ctx, NULL, NULL, MBEDTLS_RSA_PUBLIC,
+                                           digest, 0, hash_result, result_str ) == result );
 
 exit:
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &E );
     mbedtls_rsa_free( &ctx );
 }
 /* END_CASE */
@@ -225,16 +227,19 @@ void pkcs1_rsassa_pss_verify_ext( int mod,
     unsigned char result_str[1000];
     mbedtls_rsa_context ctx;
     size_t msg_len, hash_len;
+    mbedtls_mpi N, E;
 
+    mbedtls_mpi_init( &N ); mbedtls_mpi_init( &E );
     mbedtls_rsa_init( &ctx, MBEDTLS_RSA_PKCS_V21, ctx_hash );
     memset( message_str, 0x00, 1000 );
     memset( hash_result, 0x00, 1000 );
     memset( result_str, 0x00, 1000 );
 
-    ctx.len = mod / 8 + ( ( mod % 8 ) ? 1 : 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &N, radix_N, input_N ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.N, radix_N, input_N ) == 0 );
+    TEST_ASSERT( mbedtls_mpi_read_string( &E, radix_E, input_E ) == 0 );
-    TEST_ASSERT( mbedtls_mpi_read_string( &ctx.E, radix_E, input_E ) == 0 );
 
+    TEST_ASSERT( mbedtls_rsa_import( &ctx, &N, NULL, NULL, NULL, &E ) == 0 );
+    TEST_ASSERT( mbedtls_rsa_get_len( &ctx ) == (size_t) ( ( mod + 7 ) / 8 ) );
     TEST_ASSERT( mbedtls_rsa_check_pubkey( &ctx ) == 0 );
 
     msg_len = unhexify( message_str, message_hex_string );
@@ -262,6 +267,7 @@ void pkcs1_rsassa_pss_verify_ext( int mod,
                                         result_str ) == result_full );
 
 exit:
+    mbedtls_mpi_free( &N ); mbedtls_mpi_free( &E );
     mbedtls_rsa_free( &ctx );
 }
 /* END_CASE */

tests/suites/test_suite_pkparse.data

@@ -485,4 +485,4 @@ Key ASN1 (RSAPrivateKey, values present, length mismatch)
 pk_parse_key_rsa:"301c02010002010102010102010102010102010102010102010102010100":"":MBEDTLS_ERR_PK_KEY_INVALID_FORMAT
 
 Key ASN1 (RSAPrivateKey, values present, check_privkey fails)
-pk_parse_key_rsa:"301b020100020101020101020101020101020101020101020101020101":"":MBEDTLS_ERR_PK_KEY_INVALID_FORMAT
+pk_parse_key_rsa:"301b020100020102020101020101020101020101020101020101020101":"":MBEDTLS_ERR_PK_KEY_INVALID_FORMAT

tests/suites/test_suite_rsa.data

@@ -274,12 +274,15 @@ RSA Check Private key #6 (No D)
 mbedtls_rsa_check_privkey:2048:16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"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
 
 RSA Check Private key #7 (No DP)
+depends_on:!MBEDTLS_RSA_NO_CRT
 mbedtls_rsa_check_privkey:2048:16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"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
 
 RSA Check Private key #8 (No DQ)
+depends_on:!MBEDTLS_RSA_NO_CRT
 mbedtls_rsa_check_privkey:2048:16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"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
 
 RSA Check Private key #9 (No QP)
+depends_on:!MBEDTLS_RSA_NO_CRT
 mbedtls_rsa_check_privkey:2048:16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"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
 
 RSA Check Private key #10 (Incorrect)
@@ -370,6 +373,201 @@ RSA Generate Key - 1025 bit key
 # mbedtls_rsa_gen_key only supports even-sized keys
 mbedtls_rsa_gen_key:1025:3:MBEDTLS_ERR_RSA_BAD_INPUT_DATA
 
+RSA Validate Params, toy example
+mbedtls_rsa_validate_params:10:"15":10:"3":10:"5":10:"3":10:"3":0:0
+
+RSA Validate Params, toy example, N missing
+mbedtls_rsa_validate_params:10:"":10:"3":10:"5":10:"3":10:"3":0:0
+
+RSA Validate Params, toy example, E missing
+mbedtls_rsa_validate_params:10:"15":10:"3":10:"5":10:"3":10:"":0:0
+
+RSA Validate Params, toy example, corrupted
+mbedtls_rsa_validate_params:10:"16":10:"3":10:"5":10:"3":10:"3":0:MBEDTLS_ERR_RSA_KEY_CHECK_FAILED
+
+RSA Validate Params, toy example, non-primes, no PRNG
+mbedtls_rsa_validate_params:10:"45":10:"9":10:"5":10:"7":10:"23":0:0
+
+RSA Validate Params, toy example, non-primes, PRNG
+mbedtls_rsa_validate_params:10:"45":10:"9":10:"5":10:"7":10:"23":1:MBEDTLS_ERR_RSA_KEY_CHECK_FAILED
+
+RSA Validate Params
+mbedtls_rsa_validate_params:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Validate Params, N missing
+mbedtls_rsa_validate_params:16:"":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Validate Params, bad N
+mbedtls_rsa_validate_params:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Validate Params, non-prime, no PRNG
+mbedtls_rsa_validate_params:16:"":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd18":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"":0:0
+
+RSA Validate Params, non-prime, PRNG
+mbedtls_rsa_validate_params:16:"":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd18":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"":1:MBEDTLS_ERR_RSA_KEY_CHECK_FAILED
+
+RSA Deduce Private, toy example
+mbedtls_rsa_deduce_private_exponent:10:"7":10:"11":10:"7":10:"13":0:0
+
+RSA Deduce Private, toy example, corrupted
+mbedtls_rsa_deduce_private_exponent:10:"3":10:"5":10:"3":10:"3":1:MBEDTLS_ERR_MPI_NOT_ACCEPTABLE
+
+RSA Deduce Private
+mbedtls_rsa_deduce_private_exponent:16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"3":16:"77B1D99300D6A54E864962DA09AE10CF19A7FB888456BC2672B72AEA52B204914493D16C184AD201EC3F762E1FBD8702BA796EF953D9EA2F26300D285264F11B0C8301D0207FEB1E2C984445C899B0ACEBAA74EF014DD1D4BDDB43202C08D2FF9692D8D788478DEC829EB52AFB5AE068FBDBAC499A27FACECC391E75C936D55F07BB45EE184DAB45808E15722502F279F89B38C1CB292557E5063597F52C75D61001EDC33F4739353E33E56AD273B067C1A2760208529EA421774A5FFFCB3423B1E0051E7702A55D80CBF2141569F18F87BFF538A1DA8EDBB2693A539F68E0D62D77743F89EACF3B1723BDB25CE2F333FA63CACF0E67DF1A431893BB9B352FCB":0:0
+
+RSA Deduce Private, corrupted
+mbedtls_rsa_deduce_private_exponent:16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Deduce Primes, toy example
+mbedtls_rsa_deduce_primes:10:"35":10:"5":10:"5":10:"5":10:"7":0:0
+
+RSA Deduce Primes, toy example, corrupted
+mbedtls_rsa_deduce_primes:10:"35":10:"5":10:"5":10:"5":10:"7":1:MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
+RSA Deduce Moduli
+mbedtls_rsa_deduce_primes:16:"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e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":0:0
+
+RSA Deduce Moduli, corrupted
+mbedtls_rsa_deduce_primes:16:"b38ac65c8141f7f5c96e14470e851936a67bf94cc6821a39ac12c05f7c0b06d9e6ddba2224703b02e25f31452f9c4a8417b62675fdc6df46b94813bc7b9769a892c482b830bfe0ad42e46668ace68903617faf6681f4babf1cc8e4b0420d3c7f61dc45434c6b54e2c3ee0fc07908509d79c9826e673bf8363255adb0add2401039a7bcd1b4ecf0fbe6ec8369d2da486eec59559dd1d54c9b24190965eafbdab203b35255765261cd0909acf93c3b8b8428cbb448de4715d1b813d0c94829c229543d391ce0adab5351f97a3810c1f73d7b1458b97daed4209c50e16d064d2d5bfda8c23893d755222793146d0a78c3d64f35549141486c3b0961a7b4c1a2034f":16:"77B1D99300D6A54E864962DA09AE10CF19A7FB888456BC2672B72AEA52B204914493D16C184AD201EC3F762E1FBD8702BA796EF953D9EA2F26300D285264F11B0C8301D0207FEB1E2C984445C899B0ACEBAA74EF014DD1D4BDDB43202C08D2FF9692D8D788478DEC829EB52AFB5AE068FBDBAC499A27FACECC391E75C936D55F07BB45EE184DAB45808E15722502F279F89B38C1CB292557E5063597F52C75D61001EDC33F4739353E33E56AD273B067C1A2760208529EA421774A5FFFCB3423B1E0051E7702A55D80CBF2141569F18F87BFF538A1DA8EDBB2693A539F68E0D62D77743F89EACF3B1723BDB25CE2F333FA63CACF0E67DF1A431893BB9B352FCB":16:"3":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":1:MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
+RSA Import (N,P,Q,D,E)
+mbedtls_rsa_import:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Import (N,P,Q,D,E), inconsistent
+mbedtls_rsa_import:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Import (N,P,Q,D,E), successive
+mbedtls_rsa_import:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Import (N,P,Q,D,E), successive, inconsistent
+mbedtls_rsa_import:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Import (-,P,Q,D,E)
+mbedtls_rsa_import:16:"":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Import (-,P,Q,D,E), successive
+mbedtls_rsa_import:16:"":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"77B1D99300D6A54E864962DA09AE10CF19A7FB888456BC2672B72AEA52B204914493D16C184AD201EC3F762E1FBD8702BA796EF953D9EA2F26300D285264F11B0C8301D0207FEB1E2C984445C899B0ACEBAA74EF014DD1D4BDDB43202C08D2FF9692D8D788478DEC829EB52AFB5AE068FBDBAC499A27FACECC391E75C936D55F07BB45EE184DAB45808E15722502F279F89B38C1CB292557E5063597F52C75D61001EDC33F4739353E33E56AD273B067C1A2760208529EA421774A5FFFCB3423B1E0051E7702A55D80CBF2141569F18F87BFF538A1DA8EDBB2693A539F68E0D62D77743F89EACF3B1723BDB25CE2F333FA63CACF0E67DF1A431893BB9B352FCB":16:"3":1:1:0:0
+
+RSA Import (N,-,-,D,E)
+mbedtls_rsa_import:16:"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
+
+RSA Import (N,-,-,D,E), succesive
+mbedtls_rsa_import:16:"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
+
+RSA Import (N,P,Q,-,E)
+mbedtls_rsa_import:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":0:1:0:0
+
+RSA Import (N,P,Q,-,E), successive
+mbedtls_rsa_import:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":1:1:0:0
+
+RSA Import (-,P,Q,-,E)
+mbedtls_rsa_import:16:"":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":0:1:0:0
+
+RSA Import (-,P,Q,-,E), successive
+mbedtls_rsa_import:16:"":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":1:1:0:0
+
+RSA Import (N,-,Q,-,E)
+mbedtls_rsa_import:16:"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":16:"":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":0:1:0:MBEDTLS_ERR_RSA_BAD_INPUT_DATA
+
+RSA Import (N,-,Q,-,E), successive
+mbedtls_rsa_import:16:"b38ac65c8141f7f5c96e14470e851936a67bf94cc6821a39ac12c05f7c0b06d9e6ddba2224703b02e25f31452f9c4a8417b62675fdc6df46b94813bc7b9769a892c482b830bfe0ad42e46668ace68903617faf6681f4babf1cc8e4b0420d3c7f61dc45434c6b54e2c3ee0fc07908509d79c9826e673bf8363255adb0add2401039a7bcd1b4ecf0fbe6ec8369d2da486eec59559dd1d54c9b24190965eafbdab203b35255765261cd0909acf93c3b8b8428cbb448de4715d1b813d0c94829c229543d391ce0adab5351f97a3810c1f73d7b1458b97daed4209c50e16d064d2d5bfda8c23893d755222793146d0a78c3d64f35549141486c3b0961a7b4c1a2034f":16:"":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":1:1:0:MBEDTLS_ERR_RSA_BAD_INPUT_DATA
+
+RSA Import (N,-,-,-,E), complete public key
+mbedtls_rsa_import:16:"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":16:"":16:"":16:"":16:"3":0:0:0:0
+
+RSA Import (N,-,-,-,E), complete public key, successive
+mbedtls_rsa_import:16:"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":16:"":16:"":16:"":16:"3":1:0:0:0
+
+RSA Import (N,-,-,-,E), complete public key, corrupted
+mbedtls_rsa_import:16:"b38ac65c8141f7f5c96e14470e851936a67bf94cc6821a39ac12c05f7c0b06d9e6ddba2224703b02e25f31452f9c4a8417b62675fdc6df46b94813bc7b9769a892c482b830bfe0ad42e46668ace68903617faf6681f4babf1cc8e4b0420d3c7f61dc45434c6b54e2c3ee0fc07908509d79c9826e673bf8363255adb0add2401039a7bcd1b4ecf0fbe6ec8369d2da486eec59559dd1d54c9b24190965eafbdab203b35255765261cd0909acf93c3b8b8428cbb448de4715d1b813d0c94829c229543d391ce0adab5351f97a3810c1f73d7b1458b97daed4209c50e16d064d2d5bfda8c23893d755222793146d0a78c3d64f35549141486c3b0961a7b4c1a2034f":16:"":16:"":16:"":16:"4":0:0:MBEDTLS_ERR_RSA_KEY_CHECK_FAILED:0
+
+RSA Import (N,-,-,-,E), complete public key, successive, corrupted
+mbedtls_rsa_import:16:"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":16:"":16:"":16:"":16:"4":1:0:MBEDTLS_ERR_RSA_KEY_CHECK_FAILED:0
+
+RSA Import Raw (N,P,Q,D,E), complete private key
+mbedtls_rsa_import_raw:"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":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Import Raw (N,P,Q,D,E), successive
+mbedtls_rsa_import_raw:"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":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Import Raw (-,P,Q,D,E)
+mbedtls_rsa_import_raw:"":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Import Raw (-,P,Q,D,E), successive
+mbedtls_rsa_import_raw:"":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Import Raw (N,-,-,D,E)
+mbedtls_rsa_import_raw:"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
+
+RSA Import Raw (N,-,-,D,E), successive
+mbedtls_rsa_import_raw:"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
+
+RSA Import Raw (N,P,Q,-,E)
+mbedtls_rsa_import_raw:"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":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":"":"03":0:1:0:0
+
+RSA Import Raw (N,P,Q,-,E), successive
+mbedtls_rsa_import_raw:"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":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":"":"03":1:1:0:0
+
+RSA Import Raw (-,P,Q,-,E)
+mbedtls_rsa_import_raw:"":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":"":"03":0:1:0:0
+
+RSA Import Raw (-,P,Q,-,E), successive
+mbedtls_rsa_import_raw:"":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":"":"03":1:1:0:0
+
+RSA Import Raw (N,-,Q,-,E)
+mbedtls_rsa_import_raw:"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":"":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":"":"03":0:1:0:MBEDTLS_ERR_RSA_BAD_INPUT_DATA
+
+RSA Import Raw (N,-,Q,-,E), successive
+mbedtls_rsa_import_raw:"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":"":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":"":"03":1:1:0:MBEDTLS_ERR_RSA_BAD_INPUT_DATA
+
+RSA Import Raw (N,-,-,-,E)
+mbedtls_rsa_import_raw:"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":"":"":"":"03":0:0:0:0
+
+RSA Import Raw (N,-,-,-,E), successive
+mbedtls_rsa_import_raw:"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":"":"":"":"03":1:0:0:0
+
+RSA Export (N,P,Q,D,E)
+mbedtls_rsa_export:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Export (N,P,Q,D,E), successive
+mbedtls_rsa_export:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Export (N,-,-,D,E)
+mbedtls_rsa_export:16:"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
+
+RSA Export (N,-,-,D,E), succesive
+mbedtls_rsa_export:16:"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
+
+RSA Export (N,P,Q,-,E)
+mbedtls_rsa_export:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":1:0
+
+RSA Export (N,P,Q,-,E), successive
+mbedtls_rsa_export:16:"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":16:"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":16:"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":16:"":16:"3":1:1
+
+RSA Export (N,-,-,-,E)
+mbedtls_rsa_export:16:"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":16:"":16:"":16:"":16:"3":0:0
+
+RSA Export Raw (N,P,Q,D,E)
+mbedtls_rsa_export_raw:"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":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":"77B1D99300D6A54E864962DA09AE10CF19A7FB888456BC2672B72AEA52B204914493D16C184AD201EC3F762E1FBD8702BA796EF953D9EA2F26300D285264F11B0C8301D0207FEB1E2C984445C899B0ACEBAA74EF014DD1D4BDDB43202C08D2FF9692D8D788478DEC829EB52AFB5AE068FBDBAC499A27FACECC391E75C936D55F07BB45EE184DAB45808E15722502F279F89B38C1CB292557E5063597F52C75D61001EDC33F4739353E33E56AD273B067C1A2760208529EA421774A5FFFCB3423B1E0051E7702A55D80CBF2141569F18F87BFF538A1DA8EDBB2693A539F68E0D62D77743F89EACF3B1723BDB25CE2F333FA63CACF0E67DF1A431893BB9B352FCB":"03":1:0
+
+RSA Export Raw (N,P,Q,D,E), successive
+mbedtls_rsa_export_raw:"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":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e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
+
+RSA Export Raw (N,-,-,D,E)
+mbedtls_rsa_export_raw:"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
+
+RSA Export Raw (N,-,-,D,E), succesive
+mbedtls_rsa_export_raw:"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
+
+RSA Export Raw (N,P,Q,-,E)
+mbedtls_rsa_export_raw:"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":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":"":"03":1:0
+
+RSA Export Raw (N,P,Q,-,E), successive
+mbedtls_rsa_export_raw:"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":"e79a373182bfaa722eb035f772ad2a9464bd842de59432c18bbab3a7dfeae318c9b915ee487861ab665a40bd6cda560152578e8579016c929df99fea05b4d64efca1d543850bc8164b40d71ed7f3fa4105df0fb9b9ad2a18ce182c8a4f4f975bea9aa0b9a1438a27a28e97ac8330ef37383414d1bd64607d6979ac050424fd17":"c6749cbb0db8c5a177672d4728a8b22392b2fc4d3b8361d5c0d5055a1b4e46d821f757c24eef2a51c561941b93b3ace7340074c058c9bb48e7e7414f42c41da4cccb5c2ba91deb30c586b7fb18af12a52995592ad139d3be429add6547e044becedaf31fa3b39421e24ee034fbf367d11f6b8f88ee483d163b431e1654ad3e89":"":"03":1:1
+
+RSA Export Raw (N,-,-,-,E)
+mbedtls_rsa_export_raw:"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":"":"":"":"03":0:0
+
 RSA PKCS1 Encrypt Bad RNG
 depends_on:MBEDTLS_PKCS1_V15
 rsa_pkcs1_encrypt_bad_rng:"4E636AF98E40F3ADCFCCB698F4E80B9F":MBEDTLS_RSA_PKCS_V15:2048:16:"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":16:"3":"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":MBEDTLS_ERR_RSA_RNG_FAILED